{"id":1972,"date":"2020-08-21T19:41:54","date_gmt":"2020-08-21T23:41:54","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/divide-monomials\/"},"modified":"2025-09-16T14:25:39","modified_gmt":"2025-09-16T18:25:39","slug":"divide-monomials","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/divide-monomials\/","title":{"raw":"7.2 Use Quotient Property of Exponents","rendered":"7.2 Use Quotient Property of Exponents"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Simplify expressions using the Quotient Property for Exponents<\/li>\n \t<li>Simplify expressions with zero exponents<\/li>\n \t<li>Simplify expressions using the quotient to a Power Property<\/li>\n \t<li>Simplify expressions by applying several properties<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Quotient Property for Exponents<\/h1>\n<p id=\"fs-id1169596315677\">Earlier in this chapter, we developed the properties of exponents for multiplication. We summarize these properties below.<\/p>\n\n<div id=\"fs-id1169596345315\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Summary of Exponent Properties for Multiplication<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nIf \\(a\\) and \\(b\\) are real numbers, and \\(m\\) and \\(n\\) are whole numbers, then\n<table id=\"eip-756\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Product Property<\/strong><\/td>\n<td>\\({a}^{m}\\cdot {a}^{n}={a}^{m+n}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Power Property<\/strong><\/td>\n<td>\\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Product to a Power<\/strong><\/td>\n<td>\\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596217596\">Now we will look at the exponent properties for division. A quick memory refresher may help before we get started. You have learned to simplify fractions by dividing out common factors from the numerator and denominator using the Equivalent Fractions Property. This property will also help you work with algebraic fractions\u2014which are also quotients.<\/p>\n\n<div id=\"fs-id1169596302154\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Equivalent Fractions Property<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596362684\">If \\(a,b\\), and \\(c\\) are whole numbers where \\(b\\ne 0,c\\ne 0\\),<\/p>\n\n<div id=\"fs-id1169596306813\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">then \\(\\dfrac{a}{b}=\\dfrac{a\\cdot c}{b\\cdot c}\\)\u00a0 and \\(\\dfrac{a\\cdot c}{b\\cdot c}=\\dfrac{a}{b}\\)<\/div>\n<\/div>\n<\/div>\nAs before, we\u2019ll try to discover a property by looking at some examples.\n\n<\/div>\n<\/div>\n<table id=\"eip-250\" class=\"grid\" style=\"height: 82px;\" summary=\".\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">Consider<\/td>\n<td style=\"height: 16px; width: 363.906px;\">\\(\\dfrac{{x}^{5}}{{x}^{2}}\\)<\/td>\n<td style=\"height: 16px; width: 24.9062px;\">and<\/td>\n<td style=\"height: 16px; width: 298.906px;\">\\(\\dfrac{{x}^{2}}{{x}^{3}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">What do they mean?<\/td>\n<td style=\"height: 16px; width: 363.906px;\">\\(\\dfrac{x\\cdot x \\cdot x \\cdot x \\cdot x}{x\\cdot x}\\)<\/td>\n<td style=\"height: 16px; width: 24.9062px;\"><\/td>\n<td style=\"height: 16px; width: 298.906px;\">\\(\\dfrac{x \\cdot x}{x\\cdot x\\cdot x}\\)<\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 162.906px;\">Use the Equivalent Fractions Property.<\/td>\n<td style=\"height: 34px; width: 363.906px;\">\\(\\dfrac{\\overline{)x}\\cdot \\overline{)x}\\cdot x \\cdot x \\cdot x}{\\overline{)x}\\cdot \\overline{)x}}\\)<\/td>\n<td style=\"height: 34px; width: 24.9062px;\"><\/td>\n<td style=\"height: 34px; width: 298.906px;\">\\(\\dfrac{\\overline{)x}\\cdot \\overline{)x}\\cdot 1}{\\overline{)x}\\cdot \\overline{)x}\\cdot x}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">Simplify.<\/td>\n<td style=\"height: 16px; width: 363.906px;\">\\({x}^{3}\\)<\/td>\n<td style=\"height: 16px; width: 24.9062px;\"><\/td>\n<td style=\"height: 16px; width: 298.906px;\">\\(\\dfrac{1}{x}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596258488\">Notice, in each case the bases were the same and we subtracted exponents.<\/p>\n<p id=\"fs-id1169596399182\">When the larger exponent was in the numerator, we were left with factors in the numerator.<\/p>\n<p id=\"fs-id1169596373800\">When the larger exponent was in the denominator, we were left with factors in the denominator\u2014notice the numerator of 1<\/p>\n<p id=\"fs-id1169596296705\">We write:<\/p>\n\n<div id=\"fs-id1169596297593\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cc} \\dfrac{{x}^{5}}{{x}^{2}} &amp;\u00a0 \\dfrac{{x}^{2}}{{x}^{3}}\\\\\u00a0 {x}^{5-2} &amp; \\dfrac{1}{{x}^{3-2}}\u00a0 \\\\ {x}^{3} &amp; \\dfrac{1}{x}\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1169596347921\">This leads to the <em data-effect=\"italics\">Quotient Property for Exponents<\/em>.<\/p>\n\n<div id=\"fs-id1169596533211\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596229342\">If \\(a\\) is a real number, \\(a\\ne 0\\), and \\(m\\) and \\(n\\) are whole numbers, then<\/p>\n\n<div id=\"fs-id1169596263364\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n},m\\) &gt; \\(n \\) and \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}},n\\) &gt; \\(m\\)<\/div>\n<\/div>\n<\/div>\nA couple of examples with numbers may help to verify this property.\n\n\\(\\begin{array}{rlrl}\\dfrac{{3}^{4}}{{3}^{2}}&amp; = {3}^{4-2}\\hfill &amp; \\hfill \\dfrac{{5}^{2}}{{5}^{3}} &amp;= \\dfrac{1}{{5}^{3-2}} \\\\\u00a0 \\dfrac{81}{9} &amp;= {3}^{2}\\hfill &amp; \\dfrac{25}{125}&amp; = \\dfrac{1}{{5}^{1}} \\\\\u00a0 9&amp; = 9\\checkmark\\hfill &amp; \\dfrac{1}{5}&amp; = \\dfrac{1}{5}\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395711\" data-type=\"problem\">\n<p id=\"fs-id1169596391121\">Simplify: a) \\(\\frac{{x}^{9}}{{x}^{7}}\\) b) \\(\\frac{{3}^{10}}{{3}^{2}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596364357\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\nTo simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.\n<ol id=\"fs-id1168742140172\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1172184527539\" class=\"unnumbered unstyled can-break\" style=\"height: 134px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 9 is greater than 7, there are more factors of x in the numerator.\u201d In the right column is x to the ninth power divided by x to the seventh power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains x to the nine minus seventh power. One line down, the left column says \u201cSimplify.\u201d The right column contains x squared.\" width=\"574\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 510.406px;\">Since 9 &gt; 7, there are more factors of <em data-effect=\"italics\">x<\/em> in the numerator.<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184527566\" data-type=\"media\" data-alt=\"x to the ninth power divided by x to the seventh power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001a_img_new.jpg\" alt=\"x to the ninth power divided by x to the seventh power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 510.406px;\">Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}\\).<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184527625\" data-type=\"media\" data-alt=\"x to the power of 9 minus 7.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001b_img_new.jpg\" alt=\"x to the power of 9 minus 7.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 510.406px;\">Simplify.<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184642607\" data-type=\"media\" data-alt=\"x squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001c_img_new.jpg\" alt=\"x squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>\n<table id=\"eip-id1172189039496\" class=\"unnumbered unstyled can-break\" style=\"height: 126px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 10 is greater than 2, there are more factors of 3 in the numerator.\u201d In the right column is 3 to the tenth power divided by 3 squared. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains 3 to the ten minus second power. One line down, the left column says \u201cSimplify.\u201d The right column contains 3 to the eighth power.\" width=\"576\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 507.406px;\">Since 10 &gt; 2, there are more factors of <em data-effect=\"italics\">x<\/em> in the numerator.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172189039523\" data-type=\"media\" data-alt=\"3 to the tenth power divided by 3 squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002a_img_new.jpg\" alt=\"3 to the tenth power divided by 3 squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 507.406px;\">Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}\\).<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172187510348\" data-type=\"media\" data-alt=\"3 to the power of 10 minus 2.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002b_img_new.jpg\" alt=\"3 to the power of 10 minus 2.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 507.406px;\">Simplify.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172187510365\" data-type=\"media\" data-alt=\"3 to the eighth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002c_img_new.jpg\" alt=\"3 to the eighth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNotice that when the larger exponent is in the numerator, we are left with factors in the numerator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499585\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499588\" data-type=\"exercise\">\n<div id=\"fs-id1169596499590\" data-type=\"problem\">\n<p id=\"fs-id1169596499592\">Simplify: a) \\(\\dfrac{{x}^{15}}{{x}^{10}}\\) b) \\(\\dfrac{{6}^{14}}{{6}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596530725\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596541000\">a) \\({x}^{5}\\) b) \\({6}^{9}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596407582\" data-type=\"problem\">\n<p id=\"fs-id1169596407584\">Simplify: a) \\(\\dfrac{{y}^{43}}{{y}^{37}}\\) b) \\(\\dfrac{{10}^{15}}{{10}^{7}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596499808\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596499810\">a) \\({y}^{6}\\) b) \\({10}^{8}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596541022\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596407580\" data-type=\"exercise\">\n<div id=\"fs-id1169596499808\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596535578\" data-type=\"problem\">\n<p id=\"fs-id1169596370413\">Simplify: a) \\(\\dfrac{{b}^{8}}{{b}^{12}}\\) b) \\(\\dfrac{{7}^{3}}{{7}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596258577\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\nTo simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.\n<ol id=\"fs-id1168745238709\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1172187811030\" class=\"unnumbered unstyled can-break\" style=\"height: 174px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 12 is greater than 8, there are more factors of b in the denominator.\u201d In the right column is b to the eighth power divided b to the twelfth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by b to the twelve minus eighth power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by b to the fourth power.\" width=\"625\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 556.406px;\">Since 12 &gt; 8, there are more factors of <em data-effect=\"italics\">b<\/em> in the denominator.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496560\" data-type=\"media\" data-alt=\"b to the eighth power divided b to the twelfth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003a_img_new.jpg\" alt=\"b to the eighth power divided b to the twelfth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 556.406px;\">Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}}\\).<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496629\" data-type=\"media\" data-alt=\"1 divided by b to the power of 12 minus 8.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003b_img_new.jpg\" alt=\"1 divided by b to the power of 12 minus 8.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 556.406px;\">Simplify.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496646\" data-type=\"media\" data-alt=\"1 divided by b to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003c_img_new.jpg\" alt=\"1 divided by b to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>\n<table id=\"eip-id1172185594182\" class=\"unnumbered unstyled can-break\" style=\"height: 223px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 5 is greater than 3, there are more factors of b in the denominator.\u201d In the right column is 7 cubed divided 7 to the fifth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by 7 to the five minus third power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by 7 squared. One line down, the left column says \u201cSimplify\u201d again. The right column contains 1 forty ninth.\" width=\"625\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 558.406px;\">Since 5 &gt; 3, there are more factors of 3 in the denominator.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172185594208\" data-type=\"media\" data-alt=\"7 cubed divided by 7 to the fifth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004a_img_new.jpg\" alt=\"7 cubed divided by 7 to the fifth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}}\\).<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172182557346\" data-type=\"media\" data-alt=\"1 divided by 7 to the power of 5 minus 3.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004b_img_new.jpg\" alt=\"1 divided by 7 to the power of 5 minus 3.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Simplify.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172182557363\" data-type=\"media\" data-alt=\"1 divided by 7 squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004c_img_new.jpg\" alt=\"1 divided by 7 squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Simplify.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172187655614\" data-type=\"media\" data-alt=\"1 forty-ninth.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004d_img_new.jpg\" alt=\"1 forty-ninth.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNotice that when the larger exponent is in the denominator, we are left with factors in the denominator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370488\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499283\" data-type=\"exercise\">\n<div id=\"fs-id1169596499285\" data-type=\"problem\">\n<p id=\"fs-id1169596499288\">Simplify: a) \\(\\dfrac{{x}^{18}}{{x}^{22}}\\) b) \\(\\dfrac{{12}^{15}}{{12}^{30}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596497100\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596497102\">a) \\(\\dfrac{1}{{x}^{4}}\\) b) \\(\\dfrac{1}{{12}^{15}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596567678\" data-type=\"problem\">\n<p id=\"fs-id1169596567680\">Simplify: a) \\(\\dfrac{{m}^{7}}{{m}^{15}}\\) b) \\(\\dfrac{{9}^{8}}{{9}^{19}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596497596\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596362017\">a) \\(\\dfrac{1}{{m}^{8}}\\) b) \\(\\dfrac{1}{{9}^{11}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596362049\">Notice the difference in the two previous examples:<\/p>\n\n<ul id=\"fs-id1169596497125\" data-bullet-style=\"bullet\">\n \t<li>If we start with more factors in the numerator, we will end up with factors in the numerator.<\/li>\n \t<li>If we start with more factors in the denominator, we will end up with factors in the denominator.<\/li>\n<\/ul>\n<p id=\"fs-id1169596497136\">The first step in simplifying an expression using the Quotient Property for Exponents is to determine whether the exponent is larger in the numerator or the denominator.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nSimplify: a) \\(\\dfrac{{a}^{5}}{{a}^{9}}\\) b) \\(\\dfrac{{x}^{11}}{{x}^{7}}\\).\n\n<\/div>\n<div id=\"fs-id1169596368228\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745238154\" class=\"circled\" type=\"a\">\n \t<li>Is the exponent of \\(a\\) larger in the numerator or denominator? Since 9 &gt; 5, there are more \\(a\\text{'}\\text{s}\\) in the denominator and so we will end up with factors in the denominator.\n<table id=\"eip-id1172182558549\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains a to the fifth power divided by a to the ninth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by a to the nine minus fifth power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by a to the fourth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182558568\" data-type=\"media\" data-alt=\"a to the fifth power divided by a to the ninth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009a_img_new.jpg\" alt=\"a to the fifth power divided by a to the ninth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}}\\).<\/td>\n<td><span id=\"eip-id1172186035890\" data-type=\"media\" data-alt=\"1 divided by a to the power of 9 minus 5.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009b_img_new.jpg\" alt=\"1 divided by a to the power of 9 minus 5.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186035906\" data-type=\"media\" data-alt=\"1 divided by a to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009c_img_new.jpg\" alt=\"1 divided by a to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>Notice there are more factors of \\(x\\) in the numerator, since 11 &gt; 7. So we will end up with factors in the numerator.\n<table id=\"eip-id1172187685760\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains x to the eleventh power divided by x to the seventh power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains x to the eleven minus seventh power. One line down, the left column says \u201cSimplify.\u201d The right column contains x to the fourth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182253196\" data-type=\"media\" data-alt=\"x to the eleventh power divided by x to the seventh power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010a_img_new.jpg\" alt=\"x to the eleventh power divided by x to the seventh power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}}\\).<\/td>\n<td><span id=\"eip-id1172182253264\" data-type=\"media\" data-alt=\"x to the power of 11 minus 7.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010b_img_new.jpg\" alt=\"x to the power of 11 minus 7.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182253281\" data-type=\"media\" data-alt=\"x to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010c_img_new.jpg\" alt=\"x to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596407628\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1169596407634\" data-type=\"problem\">\n<p id=\"fs-id1169596407636\">Simplify: a) \\(\\dfrac{{b}^{19}}{{b}^{11}}\\) b) \\(\\dfrac{{z}^{5}}{{z}^{11}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596364173\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596364175\">a) \\({b}^{8}\\) b) \\(\\dfrac{1}{{z}^{6}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299472\" data-type=\"problem\">\n<p id=\"fs-id1169596299474\">Simplify: a) \\(\\dfrac{{p}^{9}}{{p}^{17}}\\) b) \\(\\dfrac{{w}^{13}}{{w}^{9}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596314884\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596314886\">a) \\(\\dfrac{1}{{p}^{8}}\\) b) \\({w}^{4}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with an Exponent of Zero<\/h1>\n<p id=\"fs-id1169596373087\">A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like \\(\\dfrac{{a}^{m}}{{a}^{m}}\\). From your earlier work with fractions, you know that:<\/p>\n\\(\\dfrac{2}{2}=1\\dfrac{17}{17}=1\\dfrac{-43}{-43}=1\\)\n<p id=\"fs-id1169596522381\">In words, a number divided by itself is 1. So, \\(\\dfrac{x}{x}=1\\), for any \\(x\\left(x\\ne 0\\right)\\), since any number divided by itself is 1<\/p>\n<p id=\"fs-id1169596522415\">The Quotient Property for Exponents shows us how to simplify \\(\\dfrac{{a}^{m}}{{a}^{n}}\\) when \\(m\\) &gt; \\(n\\) and when \\(n\\) &lt; \\(m\\) by subtracting exponents. What if \\(m=n\\)?<\/p>\n<p id=\"fs-id1169596362502\">Consider \\(\\frac{8}{8}\\), which we know is 1<\/p>\n\n<table id=\"eip-158\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\( \\dfrac{8}{8}=1\\)<\/td>\n<\/tr>\n<tr>\n<td>Write \\(8\\) as \\({2}^{3}\\).<\/td>\n<td>\\(\\dfrac{{2}^{3}}{{2}^{3}}=1\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract exponents.<\/td>\n<td>\\( {2}^{3-3}=1\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\({2}^{0}=1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596534031\">Now we will simplify \\(\\dfrac{{a}^{m}}{{a}^{m}}\\) in two ways to lead us to the definition of the zero exponent. In general, for \\(a\\ne 0\\):<\/p>\n<span id=\"fs-id1169596534061\" data-type=\"media\" data-alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_005_img_new.jpg\" alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596534074\">We see \\(\\dfrac{{a}^{m}}{{a}^{m}}\\) simplifies to \\({a}^{0}\\) and to 1. So \\({a}^{0}=1\\).<\/p>\n\n<div id=\"fs-id1169596531077\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Zero Exponent<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596531378\">If \\(a\\) is a non-zero number, then \\({a}^{0}=1\\).<\/p>\n<p id=\"fs-id1169596531400\">Any nonzero number raised to the zero power is 1<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596531404\">In this text, we assume any variable that we raise to the zero power is not zero.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531411\" data-type=\"problem\">\n<p id=\"fs-id1169596531413\">Simplify: a) \\({9}^{0}\\) b) \\({n}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596397936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596397941\">The definition says any non-zero number raised to the zero power is 1<\/p>\n\n<table id=\"eip-501\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nUse the definition of the zero exponent.<\/td>\n<td>\\(\\begin{array}{c}{9}^{0}\\\\ 1\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nUse the definition of the zero exponent.<\/td>\n<td>\\(\\begin{array}{c}{n}^{0}\\\\ 1\\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596529728\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596529731\" data-type=\"exercise\">\n<div id=\"fs-id1169596529733\" data-type=\"problem\">\n<p id=\"fs-id1169596529735\">Simplify: a) \\({15}^{0}\\) b) \\({m}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596533793\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596533796\">a) 1 b) 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596533807\" data-type=\"problem\">\n<p id=\"fs-id1169596533809\">Simplify: a) \\({k}^{0}\\) b) \\({29}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596453819\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596453821\">a) 1 b) 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nNow that we have defined the zero exponent, we can expand all the Properties of Exponents to include whole number exponents.\n<p id=\"fs-id1169596453832\">What about raising an expression to the zero power? Let\u2019s look at \\({\\left(2x\\right)}^{0}\\). We can use the product to a power rule to rewrite this expression.<\/p>\n\n<table id=\"eip-649\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\({\\left(2x\\right)}^{0}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the product to a power rule.<\/td>\n<td>\\({2}^{0}{x}^{0}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the zero exponent property.<\/td>\n<td>\\(1\\cdot 1\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596530788\">This tells us that any nonzero expression raised to the zero power is one.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596530795\" data-type=\"problem\">\n<p id=\"fs-id1169596530797\">Simplify: a) \\({\\left(5b\\right)}^{0}\\) b) \\({\\left(-4{a}^{2}b\\right)}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596445483\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-509\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td>\\({\\left(5b\\right)}^{0}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of the zero exponent.<\/td>\n<td>\\(1\\)<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\({\\left(-4{a}^{2}b\\right)}^{0}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of the zero exponent.<\/td>\n<td>\\(1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596348897\" data-type=\"exercise\">\n<div id=\"fs-id1169596348899\" data-type=\"problem\">\n<p id=\"fs-id1169596348902\">Simplify: a) \\({\\left(11z\\right)}^{0}\\) b) \\({\\left(-11p{q}^{3}\\right)}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596311020\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596311022\">a) \\(1\\) b) \\(1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596378231\">Simplify: a) \\({\\left(-6d\\right)}^{0}\\) b) \\({\\left(-8{m}^{2}{n}^{3}\\right)}^{0}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596395644\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596395646\">a) \\(1\\) b) \\(1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Quotient to a Power Property<\/h1>\n<p id=\"fs-id1169596395666\">Now we will look at an example that will lead us to the Quotient to a Power Property.<\/p>\n\n<table id=\"eip-873\" style=\"height: 72px; width: 100%;\" summary=\".\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\"><\/td>\n<td style=\"height: 18px; width: 360.8px;\">\\({\\left(\\dfrac{x}{y}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">This means:<\/td>\n<td style=\"height: 18px; width: 360.8px;\">\\(\\dfrac{x}{y}\\cdot \\dfrac{x}{y}\\cdot \\dfrac{x}{y}\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">Multiply the fractions.<\/td>\n<td style=\"height: 18px; width: 360.8px;\">\\(\\dfrac{x\\cdot x\\cdot x}{y\\cdot y\\cdot y}\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">Write with exponents.<\/td>\n<td style=\"height: 18px; width: 360.8px;\">\\(\\dfrac{{x}^{3}}{{y}^{3}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596395595\">Notice that the exponent applies to both the numerator and the denominator.<\/p>\n\n<table id=\"eip-602\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>We write:<\/td>\n<td>\\({\\left(\\dfrac{x}{y}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{{x}^{3}}{{y}^{3}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596435748\">This leads to the <em data-effect=\"italics\">Quotient to a Power Property for Exponents<\/em>.<\/p>\n\n<div id=\"fs-id1169596435757\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient to a Power Property for Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nIf \\(a\\) and \\(b\\) are real numbers, \\(b\\ne 0\\), and \\(m\\) is a counting number, then\n<div id=\"fs-id1169596376628\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596376667\">To raise a fraction to a power, raise the numerator and denominator to that power.<\/p>\n\n<\/div>\n<p id=\"fs-id1169596376672\">An example with numbers may help you understand this property:<\/p>\n\n<div id=\"fs-id1169596376675\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{rl}{\\left(\\dfrac{2}{3}\\right)}^{3} =&amp; \\dfrac{{2}^{3}}{{3}^{3}}\\\\\\dfrac{2}{3}\\cdot \\dfrac{2}{3}\\cdot \\dfrac{2}{3} =&amp; \\dfrac{8}{27}\\\\ \\dfrac{8}{27} =&amp; \\dfrac{8}{27}\\checkmark \\end{array}\\)<\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596457351\" data-type=\"problem\">\n<p id=\"fs-id1169596457353\">Simplify: a) \\({\\left(\\dfrac{3}{7}\\right)}^{2}\\) b) \\({\\left(\\dfrac{b}{3}\\right)}^{4}\\) c) \\({\\left(\\dfrac{k}{j}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596529554\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166424879263\">a)<\/p>\n\n<table id=\"eip-id1172187678566\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains 3 sevenths in parentheses squared. One line down, the instructions in the left column say \u201cUse Quotient to a Power Property,\u201d which is defined as a divided by b in parentheses to the m power equals a to the m power divided by b to the m power. The right column contains 3 squared divided by 7 squared. One line down, the left column says \u201cSimplify.\u201d The right column contains 9 forty ninths.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187678585\" data-type=\"media\" data-alt=\"3 sevenths squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006a_img_new.jpg\" alt=\"3 sevenths squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\).<\/td>\n<td><span id=\"eip-id1172187674036\" data-type=\"media\" data-alt=\"3 squared divided by 7 squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006b_img_new.jpg\" alt=\"3 squared divided by 7 squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187674053\" data-type=\"media\" data-alt=\"9 forty-ninths.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006c_img_new.jpg\" alt=\"9 forty-ninths.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nb)\n<table id=\"eip-id1172182558335\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains b divided by 3 in parentheses squared. One line down, the instructions in the left column say \u201cUse Quotient to a Power Property,\u201d which is defined as a divided by b in parentheses to the m power equals a to the m power divided by b to the m power. The right column contains b to the fourth power divided by 3 to the fourth power. One line down, the left column says \u201cSimplify.\u201d The right column contains b to the fourth power divided by 81.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182558354\" data-type=\"media\" data-alt=\"b thirds to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007a_img_new.jpg\" alt=\"b thirds to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\).<\/td>\n<td><span id=\"eip-id1172182556553\" data-type=\"media\" data-alt=\"b to the fourth power divided by 3 to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007b_img_new.jpg\" alt=\"b to the fourth power divided by 3 to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182556570\" data-type=\"media\" data-alt=\"b to the fourth power divided by 81.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007c_img_new.jpg\" alt=\"b to the fourth power divided by 81.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nc)\n<table id=\"eip-id1172182556719\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains k divided by j in parentheses cubed. One line down, the instructions in the left column say \u201cRaise the numerator and denominator to the third power.\u201d The right column contains k cubed divided by j cubed.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182556739\" data-type=\"media\" data-alt=\"k divided by j, in parentheses, cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_008a_img_new.jpg\" alt=\"k divided by j, in parentheses, cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Raise the numerator and denominator to the third power.<\/td>\n<td><span id=\"eip-id1172182556756\" data-type=\"media\" data-alt=\"k cubed divided by j cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_008b_img_new.jpg\" alt=\"k cubed divided by j cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSimplify: a) \\({\\left(\\dfrac{5}{8}\\right)}^{2}\\) b) \\({\\left(\\dfrac{p}{10}\\right)}^{4}\\) c) \\({\\left(\\dfrac{m}{n}\\right)}^{7}\\).\n<div id=\"fs-id1169596381182\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381186\" data-type=\"exercise\">\n<div id=\"fs-id1169596386730\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596386732\">a) \\(\\dfrac{25}{64}\\) b) \\(\\dfrac{{p}^{4}}{10,000}\\) c) \\(\\dfrac{{m}^{7}}{{n}^{7}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365188\" data-type=\"problem\">\n<p id=\"fs-id1169596365190\">Simplify: a) \\({\\left(\\dfrac{1}{3}\\right)}^{3}\\) b) \\({\\left(\\dfrac{-2}{q}\\right)}^{3}\\) c) \\({\\left(\\dfrac{w}{x}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596372296\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596372298\">a) \\(\\dfrac{1}{27}\\) b) \\(\\dfrac{-8}{{q}^{3}}\\) c) \\(\\dfrac{{w}^{4}}{{x}^{4}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Applying Several Properties<\/h1>\n<p id=\"fs-id1169596361368\">We\u2019ll now summarize all the properties of exponents so they are all together to refer to as we simplify expressions using several properties. Notice that they are now defined for whole number exponents.<\/p>\n\n<div id=\"fs-id1169596361375\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Summary of Exponent Properties<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596361381\">If \\(a\\) and \\(b\\) are real numbers, and \\(m\\) and \\(n\\) are whole numbers, then<\/p>\n\n<table id=\"eip-3\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Product Property<\/strong><\/td>\n<td>\\({a}^{m}\\cdot{a}^{n}={a}^{m+n}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Power Property<\/strong><\/td>\n<td>\\({\\left({a}^{m}\\right)}^{n}={a}^{m \\cdot n}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Product to a Power<\/strong><\/td>\n<td>\\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Quotient Property<\/strong><\/td>\n<td><img class=\"alignnone wp-image-1970\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM.png\" alt=\"(a^m)\/(b^m) = a^(m-n), a not 0, m greater than n.\" width=\"203\" height=\"79\"><\/td>\n<\/tr>\n<tr>\n<td><strong>Zero Exponent Definition<\/strong><\/td>\n<td>\\({a}^{o}=1,a\\ne 0\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Quotient to a Power Property<\/strong><\/td>\n<td>\\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}},b\\ne 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360695\" data-type=\"exercise\">\n<div id=\"fs-id1169596360697\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596453969\" data-type=\"problem\">\n<p id=\"fs-id1169596453971\">Simplify: \\(\\dfrac{{\\left({y}^{4}\\right)}^{2}}{{y}^{6}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596454002\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-495\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{{\\left({y}^{4}\\right)}^{2}}{{y}^{6}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator.<\/td>\n<td>\\(\\dfrac{{y}^{8}}{{y}^{6}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td>\\({y}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360695\" data-type=\"exercise\">\n<div id=\"fs-id1169596360697\" data-type=\"problem\">\n\nSimplify: \\(\\dfrac{{\\left({m}^{5}\\right)}^{4}}{{m}^{7}}\\).\n\n<\/div>\n<div id=\"fs-id1169596360730\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596360733\">\\({m}^{13}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360753\" data-type=\"problem\">\n<p id=\"fs-id1169596360755\">Simplify: \\(\\dfrac{{\\left({k}^{2}\\right)}^{6}}{{k}^{7}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596438585\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596438587\">\\({k}^{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360746\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360751\" data-type=\"exercise\">\n<div id=\"fs-id1169596438585\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596438604\" data-type=\"problem\">\n<p id=\"fs-id1169596438606\">Simplify: \\(\\dfrac{{b}^{12}}{{\\left({b}^{2}\\right)}^{6}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596368124\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-953\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{{b}^{12}}{{\\left({b}^{2}\\right)}^{6}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator.<\/td>\n<td>\\(\\dfrac{{b}^{12}}{{b}^{12}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td>\\({b}^{0}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596403196\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596403200\" data-type=\"exercise\">\n<div id=\"fs-id1169596403203\" data-type=\"problem\">\n<p id=\"fs-id1169596403205\">Simplify: \\(\\dfrac{{n}^{12}}{{\\left({n}^{3}\\right)}^{4}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596388044\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596388046\">1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596388058\" data-type=\"problem\">\n<p id=\"fs-id1169596388060\">Simplify: \\(\\dfrac{{x}^{15}}{{\\left({x}^{3}\\right)}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596388092\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596388095\">1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596388056\" data-type=\"exercise\">\n<div id=\"fs-id1169596388092\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nSimplify: \\({\\left(\\dfrac{{y}^{9}}{{y}^{4}}\\right)}^{2}\\).\n\n<\/div>\n<div id=\"fs-id1169596399219\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-257\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\({\\left(\\dfrac{{y}^{9}}{{y}^{4}}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Remember parentheses come before exponents.\nNotice the bases are the same, so we can simplify\ninside the parentheses. Subtract the exponents.<\/td>\n<td>\\({\\left({y}^{5}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents.<\/td>\n<td>\\({y}^{10}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596529821\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596529825\" data-type=\"exercise\">\n<div id=\"fs-id1169596529827\" data-type=\"problem\">\n<p id=\"fs-id1169596529829\">Simplify: \\({\\left(\\dfrac{{r}^{5}}{{r}^{3}}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596276589\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596276591\">\\({r}^{8}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596276610\" data-type=\"problem\">\n<p id=\"fs-id1169596276612\">Simplify: \\({\\left(\\dfrac{{v}^{6}}{{v}^{4}}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596276643\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596276645\">\\({v}^{6}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531814\" data-type=\"problem\">\n<p id=\"fs-id1169596531816\">Simplify: \\({\\left(\\dfrac{{j}^{2}}{{k}^{3}}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596531847\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596531852\">Here we cannot simplify inside the parentheses first, since the bases are not the same.<\/p>\n\n<table id=\"eip-629\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\({\\left(\\dfrac{{j}^{2}}{{k}^{3}}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Raise the numberator and denominator to the third power\nusing the Quotient to a Power Property, \\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property and simplify.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596276604\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596276608\" data-type=\"exercise\">\n<div id=\"fs-id1169596276643\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369579\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596369583\" data-type=\"exercise\">\n<div id=\"fs-id1169596369585\" data-type=\"problem\">\n<p id=\"fs-id1169596381042\">Simplify: \\({\\left(\\dfrac{{a}^{3}}{{b}^{2}}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596381073\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596381075\">\\(\\dfrac{{a}^{12}}{{b}^{8}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596381104\" data-type=\"problem\">\n<p id=\"fs-id1169596381106\">Simplify: \\({\\left(\\dfrac{{q}^{7}}{{r}^{5}}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596402096\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596402098\">\\(\\dfrac{{q}^{21}}{{r}^{15}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596381097\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381102\" data-type=\"exercise\">\n<div id=\"fs-id1169596402096\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596402126\" data-type=\"problem\">\n<p id=\"fs-id1169596402128\">Simplify: \\({\\left(\\dfrac{2{m}^{2}}{5n}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596402160\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-682\" style=\"height: 228px;\" summary=\".\" width=\"100%\">\n<tbody>\n<tr>\n<td style=\"width: 300.406px;\"><\/td>\n<td style=\"width: 221.406px;\">\\({\\left(\\dfrac{2{m}^{2}}{5n}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Raise the numberator and denominator to the fourth power,\nusing the Quotient to a Power Property, \\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\).<\/td>\n<td style=\"width: 221.406px;\">\\(\\dfrac{{\\left(2{m}^{2}\\right)}^{4}}{{\\left(5n\\right)}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Raise each factor to the fourth power.<\/td>\n<td style=\"width: 221.406px;\">\\(\\dfrac{{\\left(2{m}^{2}\\right)}^{4}}{{\\left(5n\\right)}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Use the Power Property and simplify.<\/td>\n<td style=\"width: 221.406px;\">\\(\\dfrac{16{m}^{8}}{625{n}^{4}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596375225\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596375229\" data-type=\"exercise\">\n<div id=\"fs-id1169596375231\" data-type=\"problem\">\n<p id=\"fs-id1169596375233\">Simplify: \\({\\left(\\dfrac{7{x}^{3}}{9y}\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596375265\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596375268\">\\(\\dfrac{49{x}^{6}}{81{y}^{2}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372422\" data-type=\"problem\">\n<p id=\"fs-id1169596372424\">Simplify: \\({\\left(\\dfrac{3{x}^{4}}{7y}\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596372456\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596372458\">\\(\\dfrac{9{x}^{8}}{49{y}^{2}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596372417\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596372420\" data-type=\"exercise\">\n<div id=\"fs-id1169596372456\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372488\" data-type=\"problem\">\n<p id=\"fs-id1169596372490\">Simplify: \\(\\dfrac{{\\left({x}^{3}\\right)}^{4}{\\left({x}^{2}\\right)}^{5}}{{\\left({x}^{6}\\right)}^{5}}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-119\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{{\\left({x}^{3}\\right)}^{4}{\\left({x}^{2}\\right)}^{5}}{{\\left({x}^{6}\\right)}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, \\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\).<\/td>\n<td>\\(\\dfrac{\\left({x}^{12}\\right)\\left({x}^{10}\\right)}{\\left({x}^{30}\\right)}\\)<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents in the numerator.<\/td>\n<td>\\(\\dfrac{{x}^{22}}{{x}^{30}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}}\\).<\/td>\n<td>\\(\\dfrac{1}{{x}^{8}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386224\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596386227\" data-type=\"exercise\">\n<div id=\"fs-id1169596386229\" data-type=\"problem\">\n<p id=\"fs-id1169596386231\">Simplify: \\(\\dfrac{{\\left({a}^{2}\\right)}^{3}{\\left({a}^{2}\\right)}^{4}}{{\\left({a}^{4}\\right)}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596386294\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596386296\">\\(\\dfrac{1}{{a}^{6}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSimplify: \\(\\dfrac{{\\left({p}^{3}\\right)}^{4}{\\left({p}^{5}\\right)}^{3}}{{\\left({p}^{7}\\right)}^{6}}\\).\n<div id=\"fs-id1169596386294\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\\(\\dfrac{1}{{p}^{15}}\\)\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596386314\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596386318\" data-type=\"exercise\">\n<div id=\"fs-id1169596530653\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596530677\" data-type=\"problem\">\n<p id=\"fs-id1169596530679\">Simplify: \\(\\dfrac{{\\left(10{p}^{3}\\right)}^{2}}{{\\left(5p\\right)}^{3}{\\left(2{p}^{5}\\right)}^{4}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596407750\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-836\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{{\\left(10{p}^{3}\\right)}^{2}}{{\\left(5p\\right)}^{3}{\\left(2{p}^{5}\\right)}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property, \\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\).<\/td>\n<td>\\(\\dfrac{{\\left(10\\right)}^{2}{\\left({p}^{3}\\right)}^{2}}{{\\left(5\\right)}^{3}{\\left(p\\right)}^{3}{\\left(2\\right)}^{4}{\\left({p}^{5}\\right)}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, \\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\).<\/td>\n<td>\\(\\dfrac{100{p}^{6}}{125{p}^{3}\\cdot 16{p}^{20}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents in the denominator.<\/td>\n<td>\\(\\dfrac{100{p}^{6}}{125\\cdot 16{p}^{23}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\frac{1}{{a}^{n-m}}\\).<\/td>\n<td>\\(\\dfrac{100}{125\\cdot 16{p}^{17}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(\\dfrac{1}{20{p}^{17}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596435798\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596435802\" data-type=\"exercise\">\n<div id=\"fs-id1169596435804\" data-type=\"problem\">\n<p id=\"fs-id1169596435806\">Simplify: \\(\\dfrac{{\\left(3{r}^{3}\\right)}^{2}{\\left({r}^{3}\\right)}^{7}}{{\\left({r}^{3}\\right)}^{3}}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\\(9{r}^{18}\\)\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596435896\" data-type=\"problem\">\n<p id=\"fs-id1169596435898\">Simplify: \\(\\dfrac{{\\left(2{x}^{4}\\right)}^{5}}{{\\left(4{x}^{3}\\right)}^{2}{\\left({x}^{3}\\right)}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596500737\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596500739\">\\(\\dfrac{2}{x}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Divide Monomials<\/h1>\n<p id=\"fs-id1169596500758\">You have now been introduced to all the properties of exponents and used them to simplify expressions. Next, you\u2019ll see how to use these properties to divide monomials. Later, you\u2019ll use them to divide polynomials.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596500768\" data-type=\"problem\">\n\nFind the quotient: \\(56{x}^{7}\\div 8{x}^{3}\\).\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-59\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(56{x}^{7}\\div 8{x}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td>\\(\\dfrac{56{x}^{7}}{8{x}^{3}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td>\\(\\dfrac{56}{8}\\cdot \\dfrac{{x}^{7}}{{x}^{3}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>\\(7{x}^{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596541112\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596541116\" data-type=\"exercise\">\n<div id=\"fs-id1169596541118\" data-type=\"problem\">\n<p id=\"fs-id1169596541121\">Find the quotient: \\(42{y}^{9}\\div 6{y}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596541144\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596541146\">\\(7{y}^{6}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596541167\" data-type=\"problem\">\n<p id=\"fs-id1169596541170\">Find the quotient: \\(48{z}^{8}\\div 8{z}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596541193\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596541195\">\\(6{z}^{6}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596541161\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596541165\" data-type=\"exercise\">\n<div id=\"fs-id1169596541193\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFind the quotient: \\(\\dfrac{45{a}^{2}{b}^{3}}{-5a{b}^{5}}\\).\n\n<strong>Solution<\/strong>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 34.7769%;\"><\/td>\n<td style=\"width: 65.0919%;\">\\(\\dfrac{45{a}^{2}{b}^{3}}{-5a{b}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Use fraction multiplication.<\/td>\n<td style=\"width: 65.0919%;\">\\(\\dfrac{45}{-5}\\cdot\\dfrac{{a}^{2}}{a}\\cdot \\dfrac{{b}^{3}}{{b}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Simplify and use the Quotient Property.<\/td>\n<td style=\"width: 65.0919%;\">\\(-9\\cdot a\\cdot \\dfrac{1}{{b}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Multiply.<\/td>\n<td style=\"width: 65.0919%;\">\\(-\\dfrac{9a}{{b}^{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596288714\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596288718\" data-type=\"exercise\">\n<div id=\"fs-id1169596288720\" data-type=\"problem\">\n<p id=\"fs-id1169596288722\">Find the quotient: \\(\\dfrac{-72{a}^{7}{b}^{3}}{8{a}^{12}{b}^{4}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596288759\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596288761\">\\(-\\dfrac{9}{{a}^{5}b}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596555135\">Find the quotient: \\(\\dfrac{-63{c}^{8}{d}^{3}}{7{c}^{12}{d}^{2}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596555171\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596555173\">\\(\\dfrac{-9d}{{c}^{4}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596555126\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596555130\" data-type=\"exercise\">\n<div id=\"fs-id1169596555171\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596555198\" data-type=\"problem\">\n<p id=\"fs-id1169596555200\">Find the quotient: \\(\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596555232\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-374\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td>\\(\\dfrac{24}{48}\\cdot \\dfrac{{a}^{5}}{a}\\cdot \\dfrac{{b}^{3}}{{b}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>\\(\\dfrac{1}{2}\\cdot {a}^{4}\\cdot \\dfrac{1}{b}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(\\dfrac{{a}^{4}}{2b}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463637\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596463641\" data-type=\"exercise\">\n<div id=\"fs-id1169596463643\" data-type=\"problem\">\n<p id=\"fs-id1169596463645\">Find the quotient: \\(\\dfrac{16{a}^{7}{b}^{6}}{24a{b}^{8}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596463677\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596463679\">\\(\\dfrac{2{a}^{6}}{3{b}^{2}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463711\" data-type=\"problem\">\n<p id=\"fs-id1169596463713\">Find the quotient: \\(\\dfrac{27{p}^{4}{q}^{7}}{-45{p}^{12}q}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596439843\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596439845\">\\(-\\dfrac{3{q}^{6}}{5{p}^{8}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596439872\">Once you become familiar with the process and have practiced it step by step several times, you may be able to simplify a fraction in one step.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596439881\" data-type=\"problem\">\n<p id=\"fs-id1169596439883\">Find the quotient: \\(\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596439921\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596439926\">Be very careful to simplify \\(\\dfrac{14}{21}\\) by dividing out a common factor, and to simplify the variables by subtracting their exponents.<\/p>\n\n<table id=\"eip-850\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>\\(\\dfrac{2{y}^{6}}{3{x}^{4}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596429441\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596429445\" data-type=\"exercise\">\n<div id=\"fs-id1169596429447\" data-type=\"problem\">\n<p id=\"fs-id1169596429449\">Find the quotient: \\(\\dfrac{28{x}^{5}{y}^{14}}{49{x}^{9}{y}^{12}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596429486\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596429489\">\\(\\dfrac{4{y}^{2}}{7{x}^{4}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nFind the quotient: \\(\\dfrac{30{m}^{5}{n}^{11}}{48{m}^{10}{n}^{14}}\\).\n\n<\/div>\n<div id=\"fs-id1169596382998\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596383000\">\\(\\dfrac{5}{8{m}^{5}{n}^{3}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596383025\">In all examples so far, there was no work to do in the numerator or denominator before simplifying the fraction. In the next example, we\u2019ll first find the product of two monomials in the numerator before we simplify the fraction. This follows the order of operations. Remember, a fraction bar is a grouping symbol.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596383040\" data-type=\"problem\">\n<p id=\"fs-id1169596383042\">Find the quotient: \\(\\dfrac{\\left(6{x}^{2}{y}^{3}\\right)\\left(5{x}^{3}{y}^{2}\\right)}{\\left(3{x}^{4}{y}^{5}\\right)}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596457885\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-598\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{\\left(6{x}^{2}{y}^{3}\\right)\\left(5{x}^{3}{y}^{2}\\right)}{\\left(3{x}^{4}{y}^{5}\\right)}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td>\\(\\dfrac{30{x}^{5}{y}^{5}}{3{x}^{4}{y}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(10x\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596499428\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499432\" data-type=\"exercise\">\n<div id=\"fs-id1169596499434\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499428\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499432\" data-type=\"exercise\">\n<div id=\"fs-id1169596499434\" data-type=\"problem\">\n<p id=\"fs-id1169596499437\">Find the quotient: \\(\\dfrac{\\left(6{a}^{4}{b}^{5}\\right)\\left(4{a}^{2}{b}^{5}\\right)}{12{a}^{5}{b}^{8}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596499497\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596499500\">\\(2a{b}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596216000\" class=\"media-2\" data-type=\"note\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nFind the quotient: \\(\\dfrac{\\left(-12{x}^{6}{y}^{9}\\right)\\left(-4{x}^{5}{y}^{8}\\right)}{-12{x}^{10}{y}^{12}}\\).\n\n<\/div>\n<div id=\"fs-id1169596215980\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596215982\">\\(-4x{y}^{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Additional Online Resources<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1169596216008\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/25RationalExp\">Rational Expressions<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25DivideMono\">Dividing Monomials<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25DivideMono2\">Dividing Monomials 2<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169596530860\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Quotient Property for Exponents:<\/strong>\n<ul id=\"fs-id1169596530872\" data-bullet-style=\"open-circle\">\n \t<li>If \\(a\\) is a real number, \\(a\\ne 0\\), and \\(m,n\\) are whole numbers, then:\n\\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n},m\\) &gt; \\(n\\text{ and }\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{m-n}},n\\) &gt; \\(m\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">Zero Exponent<\/strong>\n<ul id=\"fs-id1169596398934\" data-bullet-style=\"open-circle\">\n \t<li>If \\(a\\) is a non-zero number, then \\({a}^{0}=1\\).<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">Quotient to a Power Property for Exponents<\/strong>:\n<ul data-bullet-style=\"open-circle\">\n \t<li>If \\(a\\) and \\(b\\) are real numbers, \\(b\\ne 0\\), and \\(m\\) is a counting number, then:\n\\({\\left(\\dfrac{a}{b}\\right)}^{m}=\\dfrac{{a}^{m}}{{b}^{m}}\\)<\/li>\n \t<li>To raise a fraction to a power, raise the numerator and denominator to that power.<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">Summary of Exponent Properties<\/strong>\n<ul id=\"fs-id1169596498071\" data-bullet-style=\"open-circle\">\n \t<li>If \\(a,b\\) are real numbers and \\(m,n\\) are whole numbers, then<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<img class=\"alignnone wp-image-1971\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM.png\" alt=\"Summary of Product, Power, Product to a Power, Quotient, Zero Exponent Definition, and Quotient to a Power Properties.\" width=\"549\" height=\"226\">\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169596411020\">Simplify Expressions Using the Quotient Property for Exponents<\/h2>\n<p id=\"fs-id1168741783233\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. a) \\(\\frac{{x}^{18}}{{x}^{3}}\\) b) \\(\\frac{{5}^{12}}{{5}^{3}}\\)<\/td>\n<td style=\"width: 50%;\">2. a) \\(\\frac{{y}^{20}}{{y}^{10}}\\) b) \\(\\frac{{7}^{16}}{{7}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. a) \\(\\frac{{p}^{21}}{{p}^{7}}\\) b) \\(\\frac{{4}^{16}}{{4}^{4}}\\)<\/td>\n<td style=\"width: 50%;\">4. a) \\(\\frac{{u}^{24}}{{u}^{3}}\\) b) \\(\\frac{{9}^{15}}{{9}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. a) \\(\\frac{{q}^{18}}{{q}^{36}}\\) b) \\(\\frac{{10}^{2}}{{10}^{3}}\\)<\/td>\n<td style=\"width: 50%;\">6. a) \\(\\frac{{t}^{10}}{{t}^{40}}\\) b) \\(\\frac{{8}^{3}}{{8}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. a) \\(\\frac{b}{{b}^{9}}\\) b) \\(\\frac{4}{{4}^{6}}\\)<\/td>\n<td style=\"width: 50%;\">8. a) \\(\\frac{x}{{x}^{7}}\\) b) \\(\\frac{10}{{10}^{3}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596533100\">Simplify Expressions with Zero Exponents<\/h2>\n<p id=\"fs-id1168741893847\">In the following exercises, simplify.<\/p>\n\n<div id=\"fs-id1169596533107\" data-type=\"exercise\">\n<div id=\"fs-id1169596533109\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 314px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596533111\">9.<\/p>\na) \\({20}^{0}\\)\nb) \\({b}^{0}\\)<\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596533145\">10.<\/p>\na) \\({13}^{0}\\)\nb) \\({k}^{0}\\)<\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169596533178\">11.<\/p>\na) \\(-{27}^{0}\\)\nb) \\(-\\left({27}^{0}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169596364869\">12.<\/p>\na) \\(-{15}^{0}\\)\nb) \\(-\\left({15}^{0}\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596364925\">13.<\/p>\na) \\({\\left(25x\\right)}^{0}\\)\nb) \\(25{x}^{0}\\)<\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596364969\">14.<\/p>\na) \\({\\left(6y\\right)}^{0}\\)\nb) \\(6{y}^{0}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596378084\">15.<\/p>\na) \\({\\left(12x\\right)}^{0}\\)\nb) \\({\\left(-56{p}^{4}{q}^{3}\\right)}^{0}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596378144\">16.<\/p>\na) \\(7{y}^{0}\\)\\({\\left(17y\\right)}^{0}\\)\nb) \\({\\left(-93{c}^{7}{d}^{15}\\right)}^{0}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596457099\">17.<\/p>\na) \\(12{n}^{0}-18{m}^{0}\\)\nb) \\({\\left(12n\\right)}^{0}-{\\left(18m\\right)}^{0}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596457176\">18.<\/p>\na) \\(15{r}^{0}-22{s}^{0}\\)\nb) \\({\\left(15r\\right)}^{0}-{\\left(22s\\right)}^{0}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Quotient to a Power Property<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168745572221\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596406536\">19.<\/p>\na) \\({\\left(\\frac{3}{4}\\right)}^{3}\\) b) \\({\\left(\\frac{p}{2}\\right)}^{5}\\) c) \\({\\left(\\frac{x}{y}\\right)}^{6}\\)<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596379809\">20.<\/p>\na) \\({\\left(\\frac{2}{5}\\right)}^{2}\\) b) \\({\\left(\\frac{x}{3}\\right)}^{4}\\) c) \\({\\left(\\frac{a}{b}\\right)}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596379922\">21.<\/p>\na) \\({\\left(\\frac{a}{3b}\\right)}^{4}\\) b) \\({\\left(\\frac{5}{4m}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596411937\">22.<\/p>\na) \\({\\left(\\frac{x}{2y}\\right)}^{3}\\) b) \\({\\left(\\frac{10}{3q}\\right)}^{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596531103\">Simplify Expressions by Applying Several Properties<\/h2>\n<p id=\"fs-id1168741799118\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 141px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">23.\u00a0\\(\\frac{{\\left({a}^{2}\\right)}^{3}}{{a}^{4}}\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">24.\u00a0\\(\\frac{{\\left({p}^{3}\\right)}^{4}}{{p}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25.\u00a0\\(\\frac{{\\left({y}^{3}\\right)}^{4}}{{y}^{10}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">26.\u00a0\\(\\frac{{\\left({x}^{4}\\right)}^{5}}{{x}^{15}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27.\u00a0\\(\\frac{{u}^{6}}{{\\left({u}^{3}\\right)}^{2}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">28.\u00a0\\(\\frac{{v}^{20}}{{\\left({v}^{4}\\right)}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. \\(\\frac{{m}^{12}}{{\\left({m}^{8}\\right)}^{3}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">30. \\(\\frac{{n}^{8}}{{\\left({n}^{6}\\right)}^{4}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. \\({\\left(\\frac{{p}^{9}}{{p}^{3}}\\right)}^{5}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">32. \\({\\left(\\frac{{q}^{8}}{{q}^{2}}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. \\({\\left(\\frac{{r}^{2}}{{r}^{6}}\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">34. \\({\\left(\\frac{{m}^{4}}{{m}^{7}}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. \\({\\left(\\frac{p}{{r}^{11}}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">36. \\({\\left(\\frac{a}{{b}^{6}}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. \\({\\left(\\frac{{w}^{5}}{{x}^{3}}\\right)}^{8}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">38. \\({\\left(\\frac{{y}^{4}}{{z}^{10}}\\right)}^{5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. \\({\\left(\\frac{2{j}^{3}}{3k}\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">40. \\({\\left(\\frac{3{m}^{5}}{5n}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">41. \\({\\left(\\frac{3{c}^{2}}{4{d}^{6}}\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">42. \\({\\left(\\frac{5{u}^{7}}{2{v}^{3}}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. \\({\\left(\\frac{{k}^{2}{k}^{8}}{{k}^{3}}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%;\">44. \\({\\left(\\frac{{j}^{2}{j}^{5}}{{j}^{4}}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. \\(\\frac{{\\left({t}^{2}\\right)}^{5}{\\left({t}^{4}\\right)}^{2}}{{\\left({t}^{3}\\right)}^{7}}\\)<\/td>\n<td style=\"width: 50%;\">46. \\(\\frac{{\\left({q}^{3}\\right)}^{6}{\\left({q}^{2}\\right)}^{3}}{{\\left({q}^{4}\\right)}^{8}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. \\(\\frac{{\\left(-2{p}^{2}\\right)}^{4}{\\left(3{p}^{4}\\right)}^{2}}{{\\left(-6{p}^{3}\\right)}^{2}}\\)<\/td>\n<td style=\"width: 50%;\">48. \\(\\frac{{\\left(-2{k}^{3}\\right)}^{2}{\\left(6{k}^{2}\\right)}^{4}}{{\\left(9{k}^{4}\\right)}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. \\(\\frac{{\\left(-4{m}^{3}\\right)}^{2}{\\left(5{m}^{4}\\right)}^{3}}{{\\left(-10{m}^{6}\\right)}^{3}}\\)<\/td>\n<td style=\"width: 50%;\">50. \\(\\frac{{\\left(-10{n}^{2}\\right)}^{3}{\\left(4{n}^{5}\\right)}^{2}}{{\\left(2{n}^{8}\\right)}^{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596397707\">Divide Monomials<\/h2>\n<p id=\"fs-id1168745578183\">In the following exercises, divide the monomials.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. \\(56{b}^{8}\\div 7{b}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">52. \\(63{v}^{10}\\div 9{v}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. \\(-88{y}^{15}\\div 8{y}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">54. \\(-72{u}^{12}\\div 12{u}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. \\(\\frac{45{a}^{6}{b}^{8}}{-15{a}^{10}{b}^{2}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">56. \\(\\frac{54{x}^{9}{y}^{3}}{-18{x}^{6}{y}^{15}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. \\(\\frac{15{r}^{4}{s}^{9}}{18{r}^{9}{s}^{2}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">58. \\(\\frac{20{m}^{8}{n}^{4}}{30{m}^{5}{n}^{9}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. \\(\\frac{18{a}^{4}{b}^{8}}{-27{a}^{9}{b}^{5}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">60. \\(\\frac{45{x}^{5}{y}^{9}}{-60{x}^{8}{y}^{6}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. \\(\\frac{64{q}^{11}{r}^{9}{s}^{3}}{48{q}^{6}{r}^{8}{s}^{5}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">62. \\(\\frac{65{a}^{10}{b}^{8}{c}^{5}}{42{a}^{7}{b}^{6}{c}^{8}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. \\(\\frac{\\left(10{m}^{5}{n}^{4}\\right)\\left(5{m}^{3}{n}^{6}\\right)}{25{m}^{7}{n}^{5}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">64. \\(\\frac{\\left(-18{p}^{4}{q}^{7}\\right)\\left(-6{p}^{3}{q}^{8}\\right)}{-36{p}^{12}{q}^{10}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. \\(\\frac{\\left(6{a}^{4}{b}^{3}\\right)\\left(4a{b}^{5}\\right)}{\\left(12{a}^{2}b\\right)\\left({a}^{3}b\\right)}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">66. \\(\\frac{\\left(4{u}^{2}{v}^{5}\\right)\\left(15{u}^{3}v\\right)}{\\left(12{u}^{3}v\\right)\\left({u}^{4}v\\right)}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596410134\">Mixed Practice<\/h2>\n<div id=\"fs-id1169596410140\" data-type=\"exercise\">\n<div id=\"fs-id1169596410142\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 313px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 139px;\">\n<td style=\"width: 50%; height: 139px;\">\n<div id=\"fs-id1169596410140\" data-type=\"exercise\">\n<div id=\"fs-id1169596410142\" data-type=\"problem\">\n<p id=\"fs-id1169596410144\">67.<\/p>\na) \\(24{a}^{5}+2{a}^{5}\\)\nb) \\(24{a}^{5}-2{a}^{5}\\)\nc) \\(24{a}^{5}\\dot 2{a}^{5}\\)\nd) \\(24{a}^{5}\\div 2{a}^{5}\\)\n\n<\/div>\n<\/div>\n<div id=\"fs-id1169596410270\" data-type=\"exercise\">\n<div id=\"fs-id1169596410272\" data-type=\"problem\">\n<p id=\"fs-id1169596410274\"><\/p>\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 50%; height: 139px;\">\n<p id=\"fs-id1169596363438\">69.<\/p>\na) \\({p}^{4}\\cdot {p}^{6}\\)\nb) \\({\\left({p}^{4}\\right)}^{6}\\)<\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596382448\">70.<\/p>\na) \\({q}^{5}\\cdot {q}^{3}\\)\nb) \\({\\left({q}^{5}\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596382516\">71.<\/p>\na) \\(\\frac{{y}^{3}}{y}\\)\nb) \\(\\frac{y}{{y}^{3}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596382577\">72.<\/p>\na) \\(\\frac{{z}^{6}}{{z}^{5}}\\)\nb) \\(\\frac{{z}^{5}}{{z}^{6}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">73.\u00a0\\(\\left(8{x}^{5}\\right)\\left(9x\\right)\\div 6{x}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">74. \\(\\left(4y\\right)\\left(12{y}^{7}\\right)\\div 8{y}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">75. \\(\\frac{27{a}^{7}}{3{a}^{3}}+\\frac{54{a}^{9}}{9{a}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">76. \\(\\frac{32{c}^{11}}{4{c}^{5}}+\\frac{42{c}^{9}}{6{c}^{3}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">77. \\(\\frac{32{y}^{5}}{8{y}^{2}}-\\frac{60{y}^{10}}{5{y}^{7}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">78. \\(\\frac{48{x}^{6}}{6{x}^{4}}-\\frac{35{x}^{9}}{7{x}^{7}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">79. \\(\\frac{63{r}^{6}{s}^{3}}{9{r}^{4}{s}^{2}}-\\frac{72{r}^{2}{s}^{2}}{6s}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">80. \\(\\frac{56{y}^{4}{z}^{5}}{7{y}^{3}{z}^{3}}-\\frac{45{y}^{2}{z}^{2}}{5y}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">81.<strong data-effect=\"bold\"> Memory<\/strong> One megabyte is approximately \\({10}^{6}\\) bytes. One gigabyte is approximately \\({10}^{9}\\) bytes. How many megabytes are in one gigabyte?<\/td>\n<td style=\"width: 50%;\">82.<strong data-effect=\"bold\"> Memory<\/strong> One gigabyte is approximately \\({10}^{9}\\) bytes. One terabyte is approximately \\({10}^{12}\\) bytes. How many gigabytes are in one terabyte?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">83. Jennifer thinks the quotient \\(\\frac{{a}^{24}}{{a}^{6}}\\) simplifies to \\({a}^{4}\\). What is wrong with her reasoning?<\/td>\n<td style=\"width: 50%;\">84. Maurice simplifies the quotient \\(\\frac{{d}^{7}}{d}\\) by writing \\(\\frac{{\\overline{)d}}^{7}}{\\overline{)d}}=7\\). What is wrong with his reasoning?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">85. When Drake simplified \\(-{3}^{0}\\) and \\({\\left(-3\\right)}^{0}\\) he got the same answer. Explain how using the Order of Operations correctly gives different answers.<\/td>\n<td style=\"width: 50%;\">86. Robert thinks \\({x}^{0}\\) simplifies to 0. What would you say to convince Robert he is wrong?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 196px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">2. a) \\({y}^{10}\\) b) \\({7}^{14}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">4. a) \\({u}^{21}\\) b) \\({9}^{10}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">6. a) \\(\\frac{1}{{t}^{30}}\\) b) \\(\\frac{1}{64}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">8. a) \\(\\frac{1}{{x}^{6}}\\) b) \\(\\frac{1}{100}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">10. a) 1 b) 1<\/td>\n<td style=\"width: 50%; height: 16px;\">12. a) \\(-1\\) b) \\(-1\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">14. a) 1 b) 6<\/td>\n<td style=\"width: 50%; height: 16px;\">16. a) 7 b) 1<\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 50%; height: 34px;\">18. a) \\(-7\\) b) 0<\/td>\n<td style=\"width: 50%; height: 34px;\">20. a) \\(\\frac{4}{25}\\) b) \\(\\frac{{x}^{4}}{81}\\) c) \\(\\frac{{a}^{5}}{{b}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 50%; height: 34px;\">22. a) \\(\\frac{{x}^{3}}{8{y}^{3}}\\) b) \\(\\frac{10,000}{81{q}^{4}}\\)<\/td>\n<td style=\"width: 50%; height: 34px;\">24. \\({p}^{7}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">26. \\({x}^{5}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">28. 1<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">30. \\(\\frac{1}{{n}^{12}}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">32. \\({q}^{18}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">34. \\(\\frac{1}{{m}^{12}}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">36.\u00a0\\(\\frac{{a}^{3}}{{b}^{18}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">38. \\(\\frac{{y}^{20}}{{z}^{50}}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">40. \\(\\frac{27{m}^{15}}{125{n}^{3}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">42. \\(\\frac{625{u}^{28}}{16{v}^{{}^{12}}}\\)<\/td>\n<td style=\"width: 50%;\">44. \\({j}^{9}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">46. \\(\\frac{1}{{q}^{8}}\\)<\/td>\n<td style=\"width: 50%;\">48. \\(64{k}^{6}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">50. \\(-4,000\\)<\/td>\n<td style=\"width: 50%;\">52. \\(7{v}^{8}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">54. \\(-6{u}^{8}\\)<\/td>\n<td style=\"width: 50%;\">56. \\(-\\frac{3{x}^{3}}{{y}^{12}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">58. \\(\\frac{-2{m}^{3}}{3{n}^{5}}\\)<\/td>\n<td style=\"width: 50%;\">60. \\(\\frac{-3{y}^{3}}{4{x}^{3}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">62. \\(\\frac{65{a}^{3}{b}^{2}}{42{c}^{3}}\\)<\/td>\n<td style=\"width: 50%;\">64. \\(\\frac{-3{q}^{5}}{{p}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">66. \\(\\frac{5{v}^{4}}{{u}^{2}}\\)<\/td>\n<td style=\"width: 50%;\">68.\n\na) \\(18{n}^{10}\\)\nb) \\(12{n}^{10}\\)\nc) \\(45{n}^{20}\\)\nd) 5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">70.\n<div id=\"fs-id1169596382444\" data-type=\"exercise\">\n<div id=\"fs-id1169596382487\" data-type=\"solution\">\n<p id=\"fs-id1169596382489\">a) \\({q}^{8}\\)\nb) \\({q}^{15}\\)<\/p>\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 50%;\">72. a) \\(z\\) b) \\(\\frac{1}{z}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">74. \\(6{y}^{6}\\)<\/td>\n<td style=\"width: 50%;\">76. \\(15{c}^{6}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">78. \\(3{x}^{2}\\)<\/td>\n<td style=\"width: 50%;\">80. \\(-y{z}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">82. \\({10}^{3}\\)<\/td>\n<td style=\"width: 50%;\">84. Answers will vary.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">86. Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cDivide Monomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\n\n<\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Simplify expressions using the Quotient Property for Exponents<\/li>\n<li>Simplify expressions with zero exponents<\/li>\n<li>Simplify expressions using the quotient to a Power Property<\/li>\n<li>Simplify expressions by applying several properties<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Quotient Property for Exponents<\/h1>\n<p id=\"fs-id1169596315677\">Earlier in this chapter, we developed the properties of exponents for multiplication. We summarize these properties below.<\/p>\n<div id=\"fs-id1169596345315\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Summary of Exponent Properties for Multiplication<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> are whole numbers, then<\/p>\n<table id=\"eip-756\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Product Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87f8dd2a8a2c94485ba8c9c3a7652da1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#43;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Power Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-55275910ceb2defdf0be9cc5b184ca7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Product to a Power<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7ed42a6ae5889598c964652c0808f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596217596\">Now we will look at the exponent properties for division. A quick memory refresher may help before we get started. You have learned to simplify fractions by dividing out common factors from the numerator and denominator using the Equivalent Fractions Property. This property will also help you work with algebraic fractions\u2014which are also quotients.<\/p>\n<div id=\"fs-id1169596302154\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Equivalent Fractions Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596362684\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"25\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> are whole numbers where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c95b1fc74be8e9624bc66bfb3e8c0da4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;&#44;&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>,<\/p>\n<div id=\"fs-id1169596306813\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2f4be0299fc6115414c4bf6a87c4766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#125;&#123;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"67\" style=\"vertical-align: -12px;\" \/>\u00a0 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56cc34b8d6c8e0fba3df5783de05895_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#125;&#123;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"67\" style=\"vertical-align: -12px;\" \/><\/div>\n<\/div>\n<\/div>\n<p>As before, we\u2019ll try to discover a property by looking at some examples.<\/p>\n<\/div>\n<\/div>\n<table id=\"eip-250\" class=\"grid\" style=\"height: 82px;\" summary=\".\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">Consider<\/td>\n<td style=\"height: 16px; width: 363.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ab42fbe71784ca1adfdf25175d34557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"height: 16px; width: 24.9062px;\">and<\/td>\n<td style=\"height: 16px; width: 298.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cc8ff7084eaa03a4789b65caeca4a54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">What do they mean?<\/td>\n<td style=\"height: 16px; width: 363.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-88c88dc78c956c3a20465683fcfdb148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;&#123;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"102\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"height: 16px; width: 24.9062px;\"><\/td>\n<td style=\"height: 16px; width: 298.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-52c53360b59fdb25c22d8550a785e696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;&#123;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"57\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 162.906px;\">Use the Equivalent Fractions Property.<\/td>\n<td style=\"height: 34px; width: 363.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec772ac1f3808d55edbcf33c4015f894_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"116\" style=\"vertical-align: -20px;\" \/><\/td>\n<td style=\"height: 34px; width: 24.9062px;\"><\/td>\n<td style=\"height: 34px; width: 298.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce3ab0ac5eb166d9a83d416c5f25dcbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"70\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 162.906px;\">Simplify.<\/td>\n<td style=\"height: 16px; width: 363.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a29a18debcfeba0c22f81de96b6c65e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 16px; width: 24.9062px;\"><\/td>\n<td style=\"height: 16px; width: 298.906px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b86d1ba5b85781ecc0bfd6208255a9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"11\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596258488\">Notice, in each case the bases were the same and we subtracted exponents.<\/p>\n<p id=\"fs-id1169596399182\">When the larger exponent was in the numerator, we were left with factors in the numerator.<\/p>\n<p id=\"fs-id1169596373800\">When the larger exponent was in the denominator, we were left with factors in the denominator\u2014notice the numerator of 1<\/p>\n<p id=\"fs-id1169596296705\">We write:<\/p>\n<div id=\"fs-id1169596297593\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-656f88de3e99676e046689333cd9e216_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#32;&#38;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#92;&#32;&#32;&#123;&#120;&#125;&#94;&#123;&#53;&#45;&#50;&#125;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#45;&#50;&#125;&#125;&#32;&#32;&#92;&#92;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#120;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"90\" style=\"vertical-align: -51px;\" \/><\/div>\n<p id=\"fs-id1169596347921\">This leads to the <em data-effect=\"italics\">Quotient Property for Exponents<\/em>.<\/p>\n<div id=\"fs-id1169596533211\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596229342\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a real number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> are whole numbers, then<\/p>\n<div id=\"fs-id1169596263364\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d388c5467ca8f0ee93f59d2cca11eaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc33298a92b30a494ba4671aff7425b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/div>\n<\/div>\n<p>A couple of examples with numbers may help to verify this property.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ccdcdaccdfbd05d9cf609f7177900e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#108;&#114;&#108;&#125;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#51;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;&#38;&#32;&#61;&#32;&#123;&#51;&#125;&#94;&#123;&#52;&#45;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#53;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#125;&#32;&#38;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#51;&#45;&#50;&#125;&#125;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#125;&#123;&#57;&#125;&#32;&#38;&#61;&#32;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#50;&#53;&#125;&#38;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#49;&#125;&#125;&#32;&#92;&#92;&#32;&#32;&#57;&#38;&#32;&#61;&#32;&#57;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#38;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"207\" style=\"vertical-align: -51px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395711\" data-type=\"problem\">\n<p id=\"fs-id1169596391121\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-128aff1009b0a140bea9928233a96760_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"15\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-961c23dd5687b69e42cd8c1dbf566b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#51;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"20\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596364357\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p>To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.<\/p>\n<ol id=\"fs-id1168742140172\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1172184527539\" class=\"unnumbered unstyled can-break\" style=\"height: 134px; width: 574px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 9 is greater than 7, there are more factors of x in the numerator.\u201d In the right column is x to the ninth power divided by x to the seventh power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains x to the nine minus seventh power. One line down, the left column says \u201cSimplify.\u201d The right column contains x squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 510.406px;\">Since 9 &gt; 7, there are more factors of <em data-effect=\"italics\">x<\/em> in the numerator.<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184527566\" data-type=\"media\" data-alt=\"x to the ninth power divided by x to the seventh power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001a_img_new.jpg\" alt=\"x to the ninth power divided by x to the seventh power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 510.406px;\">Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2ee504c1c2fbfe39cf98068b52c3c2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"88\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184527625\" data-type=\"media\" data-alt=\"x to the power of 9 minus 7.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001b_img_new.jpg\" alt=\"x to the power of 9 minus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 510.406px;\">Simplify.<\/td>\n<td style=\"width: 33.4062px;\"><span id=\"eip-id1172184642607\" data-type=\"media\" data-alt=\"x squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_001c_img_new.jpg\" alt=\"x squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table id=\"eip-id1172189039496\" class=\"unnumbered unstyled can-break\" style=\"height: 126px; width: 576px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 10 is greater than 2, there are more factors of 3 in the numerator.\u201d In the right column is 3 to the tenth power divided by 3 squared. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains 3 to the ten minus second power. One line down, the left column says \u201cSimplify.\u201d The right column contains 3 to the eighth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 507.406px;\">Since 10 &gt; 2, there are more factors of <em data-effect=\"italics\">x<\/em> in the numerator.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172189039523\" data-type=\"media\" data-alt=\"3 to the tenth power divided by 3 squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002a_img_new.jpg\" alt=\"3 to the tenth power divided by 3 squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 507.406px;\">Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2ee504c1c2fbfe39cf98068b52c3c2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"88\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172187510348\" data-type=\"media\" data-alt=\"3 to the power of 10 minus 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002b_img_new.jpg\" alt=\"3 to the power of 10 minus 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 507.406px;\">Simplify.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172187510365\" data-type=\"media\" data-alt=\"3 to the eighth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_002c_img_new.jpg\" alt=\"3 to the eighth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that when the larger exponent is in the numerator, we are left with factors in the numerator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499585\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499588\" data-type=\"exercise\">\n<div id=\"fs-id1169596499590\" data-type=\"problem\">\n<p id=\"fs-id1169596499592\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ddf98a4684289178e19f5188432f38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"25\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-13b667b37895b0b3d804fb45765658bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#54;&#125;&#94;&#123;&#49;&#52;&#125;&#125;&#123;&#123;&#54;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596530725\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596541000\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48541f82788d9b97a870606bd6257cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-add25dc34382883048312c9ed30c0700_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596407582\" data-type=\"problem\">\n<p id=\"fs-id1169596407584\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5f77cdbbc36565e86b30bce15eba82a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#51;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"24\" style=\"vertical-align: -16px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-080a3abded8e0db65266b5199b07e0a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"33\" style=\"vertical-align: -13px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499808\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499810\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9060d39682be0df4477f1a5b1986aa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e4eb80f131277c26b1d2c29cbf8b615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596541022\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596407580\" data-type=\"exercise\">\n<div id=\"fs-id1169596499808\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596535578\" data-type=\"problem\">\n<p id=\"fs-id1169596370413\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-280bf65d20a2f49e8bb0209c2b61aaef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"23\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf182e3300344524806cb03597e4029d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#55;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#55;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"17\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596258577\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p>To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.<\/p>\n<ol id=\"fs-id1168745238709\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1172187811030\" class=\"unnumbered unstyled can-break\" style=\"height: 174px; width: 625px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 12 is greater than 8, there are more factors of b in the denominator.\u201d In the right column is b to the eighth power divided b to the twelfth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by b to the twelve minus eighth power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by b to the fourth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 556.406px;\">Since 12 &gt; 8, there are more factors of <em data-effect=\"italics\">b<\/em> in the denominator.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496560\" data-type=\"media\" data-alt=\"b to the eighth power divided b to the twelfth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003a_img_new.jpg\" alt=\"b to the eighth power divided b to the twelfth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 556.406px;\">Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec79eaf6e2d5f9b5f2224c4ca857436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496629\" data-type=\"media\" data-alt=\"1 divided by b to the power of 12 minus 8.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003b_img_new.jpg\" alt=\"1 divided by b to the power of 12 minus 8.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 556.406px;\">Simplify.<\/td>\n<td style=\"width: 38.4062px;\"><span id=\"eip-id1172184496646\" data-type=\"media\" data-alt=\"1 divided by b to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_003c_img_new.jpg\" alt=\"1 divided by b to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table id=\"eip-id1172185594182\" class=\"unnumbered unstyled can-break\" style=\"height: 223px; width: 625px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cSince 5 is greater than 3, there are more factors of b in the denominator.\u201d In the right column is 7 cubed divided 7 to the fifth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by 7 to the five minus third power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by 7 squared. One line down, the left column says \u201cSimplify\u201d again. The right column contains 1 forty ninth.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 558.406px;\">Since 5 &gt; 3, there are more factors of 3 in the denominator.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172185594208\" data-type=\"media\" data-alt=\"7 cubed divided by 7 to the fifth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004a_img_new.jpg\" alt=\"7 cubed divided by 7 to the fifth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec79eaf6e2d5f9b5f2224c4ca857436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172182557346\" data-type=\"media\" data-alt=\"1 divided by 7 to the power of 5 minus 3.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004b_img_new.jpg\" alt=\"1 divided by 7 to the power of 5 minus 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Simplify.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172182557363\" data-type=\"media\" data-alt=\"1 divided by 7 squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004c_img_new.jpg\" alt=\"1 divided by 7 squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 558.406px;\">Simplify.<\/td>\n<td style=\"width: 36.4062px;\"><span id=\"eip-id1172187655614\" data-type=\"media\" data-alt=\"1 forty-ninth.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_004d_img_new.jpg\" alt=\"1 forty-ninth.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that when the larger exponent is in the denominator, we are left with factors in the denominator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370488\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499283\" data-type=\"exercise\">\n<div id=\"fs-id1169596499285\" data-type=\"problem\">\n<p id=\"fs-id1169596499288\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9dfc5908870e417754761830a2a86d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#56;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"25\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecc3a17402e0a026b7709a3c4a0d5251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#50;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#123;&#49;&#50;&#125;&#94;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"33\" style=\"vertical-align: -13px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497100\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596497102\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1da61665a73f48bb2d54b9bcba23858f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32dc6d65e079f3c86afe9f2a12e09805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#50;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"33\" style=\"vertical-align: -13px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596567678\" data-type=\"problem\">\n<p id=\"fs-id1169596567680\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c658731e33718ddc3f95a00f4bf7a170_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"31\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7cc72331bd5225b66e9326008c1fdced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#57;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#57;&#125;&#94;&#123;&#49;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497596\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596362017\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-03817fdc2cf06b16456a912caea91da3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"24\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-52b3637fde923c339039c2a27dd2d00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#57;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"24\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596362049\">Notice the difference in the two previous examples:<\/p>\n<ul id=\"fs-id1169596497125\" data-bullet-style=\"bullet\">\n<li>If we start with more factors in the numerator, we will end up with factors in the numerator.<\/li>\n<li>If we start with more factors in the denominator, we will end up with factors in the denominator.<\/li>\n<\/ul>\n<p id=\"fs-id1169596497136\">The first step in simplifying an expression using the Quotient Property for Exponents is to determine whether the exponent is larger in the numerator or the denominator.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7d21c3c717eb93fc16e5b70ff8f5a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"18\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a77c2ce828c7c41e0864b0ed405b2e37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#49;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"25\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596368228\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745238154\" class=\"circled\" type=\"a\">\n<li>Is the exponent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> larger in the numerator or denominator? Since 9 &gt; 5, there are more <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e39e57f0be0fd4218aeac1a2d70bc7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> in the denominator and so we will end up with factors in the denominator.<br \/>\n<table id=\"eip-id1172182558549\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains a to the fifth power divided by a to the ninth power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals 1 divided by a to the n minus m power. The right column contains 1 divided by a to the nine minus fifth power. One line down, the left column says \u201cSimplify.\u201d The right column contains 1 divided by a to the fourth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182558568\" data-type=\"media\" data-alt=\"a to the fifth power divided by a to the ninth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009a_img_new.jpg\" alt=\"a to the fifth power divided by a to the ninth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec79eaf6e2d5f9b5f2224c4ca857436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><span id=\"eip-id1172186035890\" data-type=\"media\" data-alt=\"1 divided by a to the power of 9 minus 5.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009b_img_new.jpg\" alt=\"1 divided by a to the power of 9 minus 5.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186035906\" data-type=\"media\" data-alt=\"1 divided by a to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_009c_img_new.jpg\" alt=\"1 divided by a to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Notice there are more factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> in the numerator, since 11 &gt; 7. So we will end up with factors in the numerator.<br \/>\n<table id=\"eip-id1172187685760\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains x to the eleventh power divided by x to the seventh power. One line down, the instructions in the left column say \u201cUse Quotient Property,\u201d which is defined as a to the m power over a to the n power equals a to the m minus n power. The right column contains x to the eleven minus seventh power. One line down, the left column says \u201cSimplify.\u201d The right column contains x to the fourth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182253196\" data-type=\"media\" data-alt=\"x to the eleventh power divided by x to the seventh power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010a_img_new.jpg\" alt=\"x to the eleventh power divided by x to the seventh power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec79eaf6e2d5f9b5f2224c4ca857436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><span id=\"eip-id1172182253264\" data-type=\"media\" data-alt=\"x to the power of 11 minus 7.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010b_img_new.jpg\" alt=\"x to the power of 11 minus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182253281\" data-type=\"media\" data-alt=\"x to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_010c_img_new.jpg\" alt=\"x to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596407628\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1169596407634\" data-type=\"problem\">\n<p id=\"fs-id1169596407636\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e95e989cadc0e80b5401bdc9a6bf1fb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#57;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"23\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5aa32a0cbaab4cf1a621b141a5f54840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596364173\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596364175\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-660831424dd5560ce9ebfad64d0b3b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebd96a1f9d5601085342a76ee4514925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"17\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299472\" data-type=\"problem\">\n<p id=\"fs-id1169596299474\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4011018bb97ffb1c35a62994dad47cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#49;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"25\" style=\"vertical-align: -16px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12d2969bbabdee6c0e69a38ead3b9c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#119;&#125;&#94;&#123;&#49;&#51;&#125;&#125;&#123;&#123;&#119;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"28\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596314884\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596314886\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-160614aeccd10edf07b393685637fb4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"18\" style=\"vertical-align: -16px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c81d21191feff661949bf03fdb11f948_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with an Exponent of Zero<\/h1>\n<p id=\"fs-id1169596373087\">A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/>. From your earlier work with fractions, you know that:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-105d31a58907b9901f5cd96e4e87bfad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#125;&#61;&#49;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#49;&#55;&#125;&#61;&#49;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#51;&#125;&#123;&#45;&#52;&#51;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"164\" style=\"vertical-align: -12px;\" \/><\/p>\n<p id=\"fs-id1169596522381\">In words, a number divided by itself is 1. So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-665caf1b4fdeec6cc3727ea2c521ab75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#120;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"44\" style=\"vertical-align: -12px;\" \/>, for any <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fbfed3bcccaa532b43763ac59774e365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#110;&#101;&#32;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\" \/>, since any number divided by itself is 1<\/p>\n<p id=\"fs-id1169596522415\">The Quotient Property for Exponents shows us how to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2de859c9fc04f344d085c0e8fbbc1dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> by subtracting exponents. What if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-88dece3773d823856db55892f4601cd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"50\" style=\"vertical-align: 0px;\" \/>?<\/p>\n<p id=\"fs-id1169596362502\">Consider <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f2ea1e2966af14aa3a36d2ac5f3fd95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>, which we know is 1<\/p>\n<table id=\"eip-158\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d34f93b1c58f0cdae08d2c4f979802d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#56;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"42\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f823039e03edb15daaff71ce826ec6de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f380a838e4c421a1dcd7e6dc4e408eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#45;&#51;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e5553b60802088fd831b029bc495768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596534031\">Now we will simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> in two ways to lead us to the definition of the zero exponent. In general, for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>:<\/p>\n<p><span id=\"fs-id1169596534061\" data-type=\"media\" data-alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_05_005_img_new.jpg\" alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596534074\">We see <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> simplifies to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8fd43f87b436f4fe4a10f792fc700a2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> and to 1. So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1169596531077\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Zero Exponent<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596531378\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a non-zero number, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1169596531400\">Any nonzero number raised to the zero power is 1<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596531404\">In this text, we assume any variable that we raise to the zero power is not zero.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531411\" data-type=\"problem\">\n<p id=\"fs-id1169596531413\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc6bccf4cdeac0222542bea48eb9154e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9bbd01233c257a27e233e80b6591034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596397936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596397941\">The definition says any non-zero number raised to the zero power is 1<\/p>\n<table id=\"eip-501\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nUse the definition of the zero exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90bbfc8a41df13be386e16ca051ae970_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#57;&#125;&#94;&#123;&#48;&#125;&#92;&#92;&#32;&#49;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"16\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nUse the definition of the zero exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e61eb43a6176828700a3c69be66d4444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#110;&#125;&#94;&#123;&#48;&#125;&#92;&#92;&#32;&#49;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596529728\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596529731\" data-type=\"exercise\">\n<div id=\"fs-id1169596529733\" data-type=\"problem\">\n<p id=\"fs-id1169596529735\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0d0bf30dd4d31bdc12b976245afa88f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#53;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-182087e0d1621da21df9f70c62fe58ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596533793\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596533796\">a) 1 b) 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596533807\" data-type=\"problem\">\n<p id=\"fs-id1169596533809\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49c83ffb91deddda2bcf0e91d8fd55f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#107;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d473adb43059335b91076858b343673_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#57;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596453819\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596453821\">a) 1 b) 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Now that we have defined the zero exponent, we can expand all the Properties of Exponents to include whole number exponents.<\/p>\n<p id=\"fs-id1169596453832\">What about raising an expression to the zero power? Let\u2019s look at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ff00100d27ae2d5ff71a5a701214b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/>. We can use the product to a power rule to rewrite this expression.<\/p>\n<table id=\"eip-649\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ff00100d27ae2d5ff71a5a701214b1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the product to a power rule.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38beb534fd290e7e5ef1755a7e6dae37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#48;&#125;&#123;&#120;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the zero exponent property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-efb1225d468601f0a1b807ff44ac230d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"29\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596530788\">This tells us that any nonzero expression raised to the zero power is one.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596530795\" data-type=\"problem\">\n<p id=\"fs-id1169596530797\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce8d370a769d186fc7c793a653f474b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"36\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cf5805d21ee12067f6161253221420d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"69\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596445483\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-509\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce8d370a769d186fc7c793a653f474b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of the zero exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cf5805d21ee12067f6161253221420d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"69\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of the zero exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596348897\" data-type=\"exercise\">\n<div id=\"fs-id1169596348899\" data-type=\"problem\">\n<p id=\"fs-id1169596348902\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d12fc97d82e9eb89240d753f124058c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"47\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b032df587df6b95bcf26ec61e5b72bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"78\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596311020\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596311022\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596378231\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d91f7eb151350b8db9b18c756466b2a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"52\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24c33a2402277a4ec0b4ea011f4f3a93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"85\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596395644\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596395646\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Quotient to a Power Property<\/h1>\n<p id=\"fs-id1169596395666\">Now we will look at an example that will lead us to the Quotient to a Power Property.<\/p>\n<table id=\"eip-873\" style=\"height: 72px; width: 100%;\" summary=\".\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\"><\/td>\n<td style=\"height: 18px; width: 360.8px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-369935c8b8ed1d31dc9225261004a1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"44\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">This means:<\/td>\n<td style=\"height: 18px; width: 360.8px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-008c59dee04ac338f118c7fb740d9c59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"65\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">Multiply the fractions.<\/td>\n<td style=\"height: 18px; width: 360.8px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80f17596b23610efa8a1f2b171977a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;&#123;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"57\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 150.683px;\">Write with exponents.<\/td>\n<td style=\"height: 18px; width: 360.8px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fea48eb0a8d80c7e17c9dda67ef38b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"18\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596395595\">Notice that the exponent applies to both the numerator and the denominator.<\/p>\n<table id=\"eip-602\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>We write:<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-369935c8b8ed1d31dc9225261004a1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"44\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fea48eb0a8d80c7e17c9dda67ef38b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"18\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596435748\">This leads to the <em data-effect=\"italics\">Quotient to a Power Property for Exponents<\/em>.<\/p>\n<div id=\"fs-id1169596435757\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient to a Power Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a counting number, then<\/p>\n<div id=\"fs-id1169596376628\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596376667\">To raise a fraction to a power, raise the numerator and denominator to that power.<\/p>\n<\/div>\n<p id=\"fs-id1169596376672\">An example with numbers may help you understand this property:<\/p>\n<div id=\"fs-id1169596376675\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a50c68142df022667362b8e6a2383272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#108;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#32;&#61;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#92;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#32;&#61;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#55;&#125;&#92;&#92;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#55;&#125;&#32;&#61;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#55;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"118\" width=\"132\" style=\"vertical-align: -54px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596457351\" data-type=\"problem\">\n<p id=\"fs-id1169596457353\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7e0a3ca4ade0ece82d28e1ffbd8d339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"43\" style=\"vertical-align: -17px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e01c788135c8160f99d9e94eeb9350aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"43\" style=\"vertical-align: -17px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-55f91d1a8e494fd45fbe2d693300b2e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#107;&#125;&#123;&#106;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"44\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596529554\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166424879263\">a)<\/p>\n<table id=\"eip-id1172187678566\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains 3 sevenths in parentheses squared. One line down, the instructions in the left column say \u201cUse Quotient to a Power Property,\u201d which is defined as a divided by b in parentheses to the m power equals a to the m power divided by b to the m power. The right column contains 3 squared divided by 7 squared. One line down, the left column says \u201cSimplify.\u201d The right column contains 9 forty ninths.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187678585\" data-type=\"media\" data-alt=\"3 sevenths squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006a_img_new.jpg\" alt=\"3 sevenths squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><span id=\"eip-id1172187674036\" data-type=\"media\" data-alt=\"3 squared divided by 7 squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006b_img_new.jpg\" alt=\"3 squared divided by 7 squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187674053\" data-type=\"media\" data-alt=\"9 forty-ninths.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_006c_img_new.jpg\" alt=\"9 forty-ninths.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<\/p>\n<table id=\"eip-id1172182558335\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains b divided by 3 in parentheses squared. One line down, the instructions in the left column say \u201cUse Quotient to a Power Property,\u201d which is defined as a divided by b in parentheses to the m power equals a to the m power divided by b to the m power. The right column contains b to the fourth power divided by 3 to the fourth power. One line down, the left column says \u201cSimplify.\u201d The right column contains b to the fourth power divided by 81.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182558354\" data-type=\"media\" data-alt=\"b thirds to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007a_img_new.jpg\" alt=\"b thirds to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><span id=\"eip-id1172182556553\" data-type=\"media\" data-alt=\"b to the fourth power divided by 3 to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007b_img_new.jpg\" alt=\"b to the fourth power divided by 3 to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182556570\" data-type=\"media\" data-alt=\"b to the fourth power divided by 81.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_007c_img_new.jpg\" alt=\"b to the fourth power divided by 81.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>c)<\/p>\n<table id=\"eip-id1172182556719\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains k divided by j in parentheses cubed. One line down, the instructions in the left column say \u201cRaise the numerator and denominator to the third power.\u201d The right column contains k cubed divided by j cubed.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182556739\" data-type=\"media\" data-alt=\"k divided by j, in parentheses, cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_008a_img_new.jpg\" alt=\"k divided by j, in parentheses, cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Raise the numerator and denominator to the third power.<\/td>\n<td><span id=\"eip-id1172182556756\" data-type=\"media\" data-alt=\"k cubed divided by j cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_05_008b_img_new.jpg\" alt=\"k cubed divided by j cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-45aea97e99d38475c770bd3da52b0940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"43\" style=\"vertical-align: -17px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-376343f5ccf4e7cea04cd233064aa81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"47\" style=\"vertical-align: -12px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6a90864e73ca3f77804a6888cf1e0a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#109;&#125;&#123;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"45\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<div id=\"fs-id1169596381182\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381186\" data-type=\"exercise\">\n<div id=\"fs-id1169596386730\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596386732\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17e539027ff7c1fb91b34b196632809f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a634a6886b492882051d18661483cde1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#49;&#48;&#44;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"53\" style=\"vertical-align: -16px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-176cb4564323b197ca3ab5ee99ded1a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365188\" data-type=\"problem\">\n<p id=\"fs-id1169596365190\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2245c3031d19d13eec25f3bdb147096d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"43\" style=\"vertical-align: -17px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2692d3507278dc6d2fe2b41cb3913ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#125;&#123;&#113;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"57\" style=\"vertical-align: -17px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a617aaccfb3d375aa1d4337a931bd2d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#119;&#125;&#123;&#120;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"42\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596372296\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596372298\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-834a152938a9e89e744659876ef63cac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc2305043ac2c86cf36eb13505fe860f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#56;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"23\" style=\"vertical-align: -16px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-45a94b31a6adfafdfaba4475f05ed8da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#119;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"21\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Applying Several Properties<\/h1>\n<p id=\"fs-id1169596361368\">We\u2019ll now summarize all the properties of exponents so they are all together to refer to as we simplify expressions using several properties. Notice that they are now defined for whole number exponents.<\/p>\n<div id=\"fs-id1169596361375\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Summary of Exponent Properties<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596361381\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> are whole numbers, then<\/p>\n<table id=\"eip-3\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Product Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49012d0c36859c40c70a3b18f0bbf4c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#43;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Power Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5dd7211b7024501f36a3e479ced640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Product to a Power<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7ed42a6ae5889598c964652c0808f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Quotient Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1970\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM.png\" alt=\"(a^m)\/(b^m) = a^(m-n), a not 0, m greater than n.\" width=\"203\" height=\"79\" srcset=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM.png 1278w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-300x117.png 300w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-1024x399.png 1024w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-768x299.png 768w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-65x25.png 65w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-225x88.png 225w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.45.27-AM-350x136.png 350w\" sizes=\"auto, (max-width: 203px) 100vw, 203px\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Zero Exponent Definition<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b9a42c26aa6e3d1aa2163ef0db4d679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#111;&#125;&#61;&#49;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Quotient to a Power Property<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6edf2a625f67c466ff1fe65d5810d8e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;&#44;&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"142\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360695\" data-type=\"exercise\">\n<div id=\"fs-id1169596360697\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596453969\" data-type=\"problem\">\n<p id=\"fs-id1169596453971\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fbadf889fcfe795db56a86b3ef181f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"41\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596454002\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-495\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fbadf889fcfe795db56a86b3ef181f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"41\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a23737603a938d91e5978ae46dee507c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"18\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f72e617ab66ab04529ce474aaeeba224_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360695\" data-type=\"exercise\">\n<div id=\"fs-id1169596360697\" data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c60831df0d2aab3881528b6a22aba87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"48\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596360730\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596360733\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4e18c9f51950952a5313c424cfff05b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360753\" data-type=\"problem\">\n<p id=\"fs-id1169596360755\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f2754d02b2627ff7ad0c458e796ffb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"42\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596438585\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596438587\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b309bfb08bc9619ef1eea5bd1268e4c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#107;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360746\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360751\" data-type=\"exercise\">\n<div id=\"fs-id1169596438585\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596438604\" data-type=\"problem\">\n<p id=\"fs-id1169596438606\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3069412f6667e30e9413f0a5410f5c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"37\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596368124\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-953\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3069412f6667e30e9413f0a5410f5c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"37\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6dd5faf3645cbe91fe4375401df5c440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"23\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-484605cd68aa07e7715ff451823e25ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596403196\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596403200\" data-type=\"exercise\">\n<div id=\"fs-id1169596403203\" data-type=\"problem\">\n<p id=\"fs-id1169596403205\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca2c9beed0d014790eb7764774c0bbb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#110;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"40\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596388044\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596388046\">1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596388058\" data-type=\"problem\">\n<p id=\"fs-id1169596388060\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-52053fd842f7ce60d647a9831fdf6e40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"40\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596388092\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596388095\">1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596388056\" data-type=\"exercise\">\n<div id=\"fs-id1169596388092\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf4a92b1961fc578d76c864b5bd53a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596399219\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-257\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf4a92b1961fc578d76c864b5bd53a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Remember parentheses come before exponents.<br \/>\nNotice the bases are the same, so we can simplify<br \/>\ninside the parentheses. Subtract the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e989c5304218cd869643a21b4f61509_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18f0c771be0f5f7f94a86466c8873ac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596529821\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596529825\" data-type=\"exercise\">\n<div id=\"fs-id1169596529827\" data-type=\"problem\">\n<p id=\"fs-id1169596529829\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34b0582aaf0479fa7783970733a6640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"50\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596276589\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596276591\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9d77a3d57f6c169d67d7532329c7e7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596276610\" data-type=\"problem\">\n<p id=\"fs-id1169596276612\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ccb3879c2d2832b3117300a2106136ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#118;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596276643\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596276645\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49ec46279e732c46559d2d02dee0bc51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#118;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531814\" data-type=\"problem\">\n<p id=\"fs-id1169596531816\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4009d94b28d1004ae7978330db09721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596531847\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596531852\">Here we cannot simplify inside the parentheses first, since the bases are not the same.<\/p>\n<table id=\"eip-629\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4009d94b28d1004ae7978330db09721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Raise the numberator and denominator to the third power<br \/>\nusing the Quotient to a Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property and simplify.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596276604\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596276608\" data-type=\"exercise\">\n<div id=\"fs-id1169596276643\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369579\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596369583\" data-type=\"exercise\">\n<div id=\"fs-id1169596369585\" data-type=\"problem\">\n<p id=\"fs-id1169596381042\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c079fc6af4348eb6424d088670e88d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"51\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596381073\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596381075\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f14133a37ff63fdae07837c571de425c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596381104\" data-type=\"problem\">\n<p id=\"fs-id1169596381106\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cfd4fe09f82254ad2d4d23274f946952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"50\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596402096\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596402098\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2bdc1bc5c46de8d6936975c5b53512a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#113;&#125;&#94;&#123;&#50;&#49;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"24\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596381097\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381102\" data-type=\"exercise\">\n<div id=\"fs-id1169596402096\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596402126\" data-type=\"problem\">\n<p id=\"fs-id1169596402128\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8448f9dd896cfd88fb7ad597b642063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#53;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"66\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596402160\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-682\" style=\"height: 228px; width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 300.406px;\"><\/td>\n<td style=\"width: 221.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8448f9dd896cfd88fb7ad597b642063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#53;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"66\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Raise the numberator and denominator to the fourth power,<br \/>\nusing the Quotient to a Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 221.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41f352949dffe4b91a5f703cc91011cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"57\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Raise each factor to the fourth power.<\/td>\n<td style=\"width: 221.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41f352949dffe4b91a5f703cc91011cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"57\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300.406px;\">Use the Power Property and simplify.<\/td>\n<td style=\"width: 221.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3555e2342cc89b5e047175d8ed9f69f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#54;&#50;&#53;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"45\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596375225\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596375229\" data-type=\"exercise\">\n<div id=\"fs-id1169596375231\" data-type=\"problem\">\n<p id=\"fs-id1169596375233\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0a7a73e058872ce06ac338fbe98b90e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#57;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"61\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596375265\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596375268\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5249868958bec83fe8c6d3304661b59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#56;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"36\" style=\"vertical-align: -16px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372422\" data-type=\"problem\">\n<p id=\"fs-id1169596372424\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c86f5b3a5ae176e813aa8085cc6b58de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#55;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"61\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596372456\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596372458\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-363d3e16b101a3a8235bb5451a70e038_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#52;&#57;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"35\" style=\"vertical-align: -16px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596372417\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596372420\" data-type=\"exercise\">\n<div id=\"fs-id1169596372456\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372488\" data-type=\"problem\">\n<p id=\"fs-id1169596372490\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6478544ea7eab6e35d6db681b332abd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"84\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-119\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6478544ea7eab6e35d6db681b332abd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"84\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-55275910ceb2defdf0be9cc5b184ca7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2df9c2478ad148b74663ef660484132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"85\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the exponents in the numerator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4d109ecc253f51ca1febcafc3928b49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"25\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec79eaf6e2d5f9b5f2224c4ca857436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"92\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8268f4d7f690de3f4ad287a06bb3e4b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386224\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596386227\" data-type=\"exercise\">\n<div id=\"fs-id1169596386229\" data-type=\"problem\">\n<p id=\"fs-id1169596386231\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc8294003d588d96b30cde4acef21ab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"83\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596386294\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596386296\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-506e413d9dea9300669613e14a6f00ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f9084115c3e93cd8ffd3084155c647fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"82\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<div id=\"fs-id1169596386294\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5ab9a17f5feb7732a0ff148d736b6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"25\" style=\"vertical-align: -16px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596386314\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596386318\" data-type=\"exercise\">\n<div id=\"fs-id1169596530653\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596530677\" data-type=\"problem\">\n<p id=\"fs-id1169596530679\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ad18a44a0ae7ae827f1b9b96a95b4e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"87\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596407750\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-836\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ad18a44a0ae7ae827f1b9b96a95b4e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"87\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7ed42a6ae5889598c964652c0808f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c8de622c94fef3a53d7f067e6c2ff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"130\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-55275910ceb2defdf0be9cc5b184ca7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37d1907b54566685d5e0ee38f24c8a8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#49;&#50;&#53;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"98\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the exponents in the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7fddb00e528ffee50865d20835a03bf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#49;&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"81\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bc51189512a870ef53a46e955d27103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-326b173723126d7ee6157079fd62ed4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#125;&#123;&#49;&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#123;&#112;&#125;&#94;&#123;&#49;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"81\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e7491ab6f2e372efef7d11ca181fb00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#48;&#123;&#112;&#125;&#94;&#123;&#49;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"42\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596435798\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596435802\" data-type=\"exercise\">\n<div id=\"fs-id1169596435804\" data-type=\"problem\">\n<p id=\"fs-id1169596435806\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8bcd42b6c8446328b940cbad8f67c227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"90\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b770230ebefd4d4944671fef6464bd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#114;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596435896\" data-type=\"problem\">\n<p id=\"fs-id1169596435898\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-841bda427423c09e086f0754db431113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"88\" style=\"vertical-align: -20px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596500737\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596500739\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4c8cd73b368b77e85495d77850389fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"11\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Divide Monomials<\/h1>\n<p id=\"fs-id1169596500758\">You have now been introduced to all the properties of exponents and used them to simplify expressions. Next, you\u2019ll see how to use these properties to divide monomials. Later, you\u2019ll use them to divide polynomials.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596500768\" data-type=\"problem\">\n<p>Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-464365685b1b3dc26b3a02d3308c1436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#92;&#100;&#105;&#118;&#32;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-59\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-464365685b1b3dc26b3a02d3308c1436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#92;&#100;&#105;&#118;&#32;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ab5afac07ee9cb7ec8b83c8e81740b17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"36\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9a829cecde9474b391bc69b83aca137_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#125;&#123;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"52\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e352430cc397458fdf85afec0242a06c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596541112\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596541116\" data-type=\"exercise\">\n<div id=\"fs-id1169596541118\" data-type=\"problem\">\n<p id=\"fs-id1169596541121\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97837507d79aa47d153f53657b619d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#92;&#100;&#105;&#118;&#32;&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596541144\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596541146\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de242f5ea1092ad05dedffe40c5a42da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596541167\" data-type=\"problem\">\n<p id=\"fs-id1169596541170\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7c2eb82c09b5164a248e5e4f3142e9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#123;&#122;&#125;&#94;&#123;&#56;&#125;&#92;&#100;&#105;&#118;&#32;&#56;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596541193\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596541195\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97b1254e0e95d690867a457314a9fcbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#122;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596541161\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596541165\" data-type=\"exercise\">\n<div id=\"fs-id1169596541193\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9faa72e4e6b7547cd75e878b2fd0c402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#45;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"51\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 34.7769%;\"><\/td>\n<td style=\"width: 65.0919%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9faa72e4e6b7547cd75e878b2fd0c402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#45;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Use fraction multiplication.<\/td>\n<td style=\"width: 65.0919%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b26d8b5d2a87acd6ef925de583fc29d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#45;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"89\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Simplify and use the Quotient Property.<\/td>\n<td style=\"width: 65.0919%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e79120bab8500a38b8b6e10f7c428a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"75\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 34.7769%;\">Multiply.<\/td>\n<td style=\"width: 65.0919%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24f1ca724b951dbf9f1ec50b54f8338d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#97;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596288714\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596288718\" data-type=\"exercise\">\n<div id=\"fs-id1169596288720\" data-type=\"problem\">\n<p id=\"fs-id1169596288722\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2535bb1e8b5622f3981e5fdcf692412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#55;&#50;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#56;&#123;&#97;&#125;&#94;&#123;&#49;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"64\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596288759\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596288761\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-616f3eccc1474b6202fd571005650544_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"40\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596555135\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8afdd949469d5f7c09e20430ea63f506_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#54;&#51;&#123;&#99;&#125;&#94;&#123;&#56;&#125;&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#55;&#123;&#99;&#125;&#94;&#123;&#49;&#50;&#125;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"64\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596555171\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596555173\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-972dc5237613f4f1d45115d1f76db600_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#57;&#100;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"33\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596555126\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596555130\" data-type=\"exercise\">\n<div id=\"fs-id1169596555171\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596555198\" data-type=\"problem\">\n<p id=\"fs-id1169596555200\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abb5ff3860b70555d654b0cc365044bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#52;&#56;&#97;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"51\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596555232\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-374\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abb5ff3860b70555d654b0cc365044bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#52;&#56;&#97;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e896038559602cbe973f8a235480f928_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#125;&#123;&#52;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"84\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-500d76433d87c10bcf68daa6b8b6b831_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29eb421a9ba3cea8c8f7e0c2141a7d40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#50;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463637\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596463641\" data-type=\"exercise\">\n<div id=\"fs-id1169596463643\" data-type=\"problem\">\n<p id=\"fs-id1169596463645\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abf10e4dd13a13f32dc4f83f825161ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#123;&#98;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#50;&#52;&#97;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"51\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596463677\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596463679\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9ae85f1f4def4ab57ff6f30472464d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"26\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463711\" data-type=\"problem\">\n<p id=\"fs-id1169596463713\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b4faa369633eb5bff60034817f1708c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#45;&#52;&#53;&#123;&#112;&#125;&#94;&#123;&#49;&#50;&#125;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"64\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596439843\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596439845\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bbdf67816e7d530e2b55f755242bf21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#53;&#123;&#112;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"41\" style=\"vertical-align: -16px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596439872\">Once you become familiar with the process and have practiced it step by step several times, you may be able to simplify a fraction in one step.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596439881\" data-type=\"problem\">\n<p id=\"fs-id1169596439883\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81ea821aab0c93775ca953565c2a3398_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#49;&#49;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"60\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596439921\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596439926\">Be very careful to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d177da0ec9c6cb6087769e6568be5c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/> by dividing out a common factor, and to simplify the variables by subtracting their exponents.<\/p>\n<table id=\"eip-850\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81ea821aab0c93775ca953565c2a3398_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#49;&#49;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"60\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cab9e668f16711c79d3191947869ac6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"27\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596429441\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596429445\" data-type=\"exercise\">\n<div id=\"fs-id1169596429447\" data-type=\"problem\">\n<p id=\"fs-id1169596429449\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1f90881764b360d1b237d85a90ab07a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#56;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#52;&#125;&#125;&#123;&#52;&#57;&#123;&#120;&#125;&#94;&#123;&#57;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"60\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596429486\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596429489\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-171a952ba06c2ff683605148f367e074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#55;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"27\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4671524163244077e1cb3e00550e077_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#49;&#49;&#125;&#125;&#123;&#52;&#56;&#123;&#109;&#125;&#94;&#123;&#49;&#48;&#125;&#123;&#110;&#125;&#94;&#123;&#49;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"74\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596382998\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596383000\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3042a2af611d9d51679ac3d224ed854b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596383025\">In all examples so far, there was no work to do in the numerator or denominator before simplifying the fraction. In the next example, we\u2019ll first find the product of two monomials in the numerator before we simplify the fraction. This follows the order of operations. Remember, a fraction bar is a grouping symbol.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596383040\" data-type=\"problem\">\n<p id=\"fs-id1169596383042\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8e6600f9159168784881f5ed928155b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"123\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596457885\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-598\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8e6600f9159168784881f5ed928155b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"123\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d3f63960ee40c96a0a74bf65d46d624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"53\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-405a623e7d2a6832578e529d3677c15a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596499428\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499432\" data-type=\"exercise\">\n<div id=\"fs-id1169596499434\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499428\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499432\" data-type=\"exercise\">\n<div id=\"fs-id1169596499434\" data-type=\"problem\">\n<p id=\"fs-id1169596499437\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d38a03b39b1f532eb487b8f4118d7738_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"118\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499497\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499500\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69554c555bc995758cbfb986926428b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596216000\" class=\"media-2\" data-type=\"note\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1da5a0c0e1c66fd05e7b79786a5ba036_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"160\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596215980\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596215982\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2455069d4c2a2262188ff2ae3710ce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#120;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Additional Online Resources<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1169596216008\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25RationalExp\">Rational Expressions<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25DivideMono\">Dividing Monomials<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25DivideMono2\">Dividing Monomials 2<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169596530860\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Quotient Property for Exponents:<\/strong>\n<ul id=\"fs-id1169596530872\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a real number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7802b180fbdc92b8b164327d508e4170_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"34\" style=\"vertical-align: -4px;\" \/> are whole numbers, then:<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d388c5467ca8f0ee93f59d2cca11eaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0396edebe223a835ea4e9b14f4271745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#97;&#110;&#100;&#32;&#125;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#125;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"165\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Zero Exponent<\/strong>\n<ul id=\"fs-id1169596398934\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a non-zero number, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Quotient to a Power Property for Exponents<\/strong>:\n<ul data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a counting number, then:<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36d7ed0e544c9610ea43259415e4efb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"93\" style=\"vertical-align: -12px;\" \/><\/li>\n<li>To raise a fraction to a power, raise the numerator and denominator to that power.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Summary of Exponent Properties<\/strong>\n<ul id=\"fs-id1169596498071\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7802b180fbdc92b8b164327d508e4170_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"34\" style=\"vertical-align: -4px;\" \/> are whole numbers, then<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1971\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM.png\" alt=\"Summary of Product, Power, Product to a Power, Quotient, Zero Exponent Definition, and Quotient to a Power Properties.\" width=\"549\" height=\"226\" srcset=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM.png 2766w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-300x124.png 300w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-1024x422.png 1024w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-768x316.png 768w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-1536x633.png 1536w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-2048x843.png 2048w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-65x27.png 65w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-225x93.png 225w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-25-at-7.55.46-AM-350x144.png 350w\" sizes=\"auto, (max-width: 549px) 100vw, 549px\" \/><\/p>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169596411020\">Simplify Expressions Using the Quotient Property for Exponents<\/h2>\n<p id=\"fs-id1168741783233\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-223df321edfb09de6e05d856bf5ed499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#56;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"21\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0aba675c898725d37329e566af033899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#53;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">2. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bd4ffdfec1af8d4f8aa8dab6968a3776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#48;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"20\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6e47091666ef7be11bda8f2bb5400f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#55;&#125;&#94;&#123;&#49;&#54;&#125;&#125;&#123;&#123;&#55;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede903546d1b70ddbc7fddecef479489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#112;&#125;&#94;&#123;&#50;&#49;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"21\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-809d726a05bc2b386c4c587b4bca9b8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#52;&#125;&#94;&#123;&#49;&#54;&#125;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">4. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f79da1542342541935cce63868c33b01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#117;&#125;&#94;&#123;&#50;&#52;&#125;&#125;&#123;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"21\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9383aaeaebf1c25084802caaa85ecf9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#57;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#123;&#57;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-09c28286d361dd440748355553db96d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#113;&#125;&#94;&#123;&#49;&#56;&#125;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#51;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"20\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1bffedea54812f2c7001ae6987c2309e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"21\" style=\"vertical-align: -8px;\" \/><\/td>\n<td style=\"width: 50%;\">6. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c10ea27c9f838f1c355145bf2dfad54e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#116;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#123;&#116;&#125;&#94;&#123;&#52;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"18\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ab62c6c8cffee07bbf1902763db5066_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#56;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#56;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a2c79663d4b1f2108773002da6d0519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"13\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6dc8e9d81bd9b5a9df4bafca4be09063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">8. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c45c4db63ff753010be0409b3b5448c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71f0bb98d7b0bdd72ce344f8268009ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"21\" style=\"vertical-align: -8px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596533100\">Simplify Expressions with Zero Exponents<\/h2>\n<p id=\"fs-id1168741893847\">In the following exercises, simplify.<\/p>\n<div id=\"fs-id1169596533107\" data-type=\"exercise\">\n<div id=\"fs-id1169596533109\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 314px;\">\n<tbody>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596533111\">9.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29235d394f359e05cc3e1232453451d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#48;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-484605cd68aa07e7715ff451823e25ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596533145\">10.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be05e5194bbaac21122ec3219b8b0a8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49c83ffb91deddda2bcf0e91d8fd55f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#107;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169596533178\">11.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d047a0723f9c4cdcd3b5fbf36ae2bb4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#50;&#55;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70b2d4de96035c8614e6bdb7f70ba812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#50;&#55;&#125;&#94;&#123;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169596364869\">12.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68ab8e348d827914387b3f9d86f0ff1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#49;&#53;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e3eb632feb8bfd49fe72c8a1a5d9591_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#49;&#53;&#125;&#94;&#123;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596364925\">13.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf04bb64bd9ddb3c0451799ca95d590d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#53;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"48\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41169d519ff46306c7b41089d948559b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596364969\">14.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-777371e45587625a74fa315a7aeb0af5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"38\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2fa486a3a1c169f6d1df722a3acd7f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596378084\">15.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da0486715fa8ac22945661e9553bccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"48\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-994eb4ecc0799fbf7c3dc99c8872f525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#54;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"86\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596378144\">16.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31f496769c61bea2d34daee8420637da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#121;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f9f1bbaa837398f7402acb5d65b8960_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#55;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"47\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bca062bd426a1d99d917b27e0ab9a7df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#51;&#123;&#99;&#125;&#94;&#123;&#55;&#125;&#123;&#100;&#125;&#94;&#123;&#49;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"92\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596457099\">17.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-539e1a63c736b6546ff73d03984f371d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#110;&#125;&#94;&#123;&#48;&#125;&#45;&#49;&#56;&#123;&#109;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ca586c317b8b9209bc12d6383e6cf0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#56;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596457176\">18.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-558fd216c8f350d44c348476c69ef036_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#114;&#125;&#94;&#123;&#48;&#125;&#45;&#50;&#50;&#123;&#115;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f087d8d83490ee4d492605716e4e06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#50;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Quotient to a Power Property<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168745572221\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596406536\">19.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af6bbe39fd1a441f3339562a057974c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d0dd94ed54008490615aed910826c62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18eb12d77cddb880d9128e2b7d280b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596379809\">20.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e5313e5ff85eb76aefa3cd3d6ae600f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0cfbb1e7fc3dc3a6b997aaa53f6a8785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"33\" style=\"vertical-align: -7px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51922f2c199f361be2975851917d2034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596379922\">21.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1dd3be93bdb59d4979075e0f28b0af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#51;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7c27339f8193d52c43a33d5f61ea0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"44\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169596411937\">22.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15d99a3d340a30355a961ac2a4aa5b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#50;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"43\" style=\"vertical-align: -12px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85ffe01eeb7a642b01e240ef62717e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#113;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"43\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596531103\">Simplify Expressions by Applying Several Properties<\/h2>\n<p id=\"fs-id1168741799118\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 141px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">23.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-316ed25b779e5e30e56f3b7772cae56a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"35\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">24.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38bfc0f8b276cb951b07bdb0958e1e46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"35\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-192d4c276b550124d87402bc0670908f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"35\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">26.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dadc4e651423f839857fd6fb11ceec2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"36\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac053b2e73cddccffcedab308db967ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#117;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"33\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">28.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2902becbf7166c0d8e941074f971bf3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#118;&#125;&#94;&#123;&#50;&#48;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"32\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f5f2880fd4ee46b43f712a8f931a5d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"37\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0bd252b183ad8fccd07103b6e4d954e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#110;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"33\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96afa50a30c6e1de6644490aff1d2cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"43\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c83e56d55e51da6c303077fdf51c919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#113;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"42\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94cd8e3b7db22f1d683ff8955565ff56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"42\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b5f343c002177f4a7d6acd1a858ca73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"48\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a7f65105fab4f9f40a4cf3528efde21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#49;&#49;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"44\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b25e9d0631096e70c8cfd62cdf335260_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#54;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4297e186c229bb5eb2a33b11299fb407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#119;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"46\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b2961e39787556300b530cfe601f4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"49\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a5bce83e17a55a98266a3e0d183a5d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#106;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#107;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"49\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14ecec262c3311115b38a4a8fcf5a042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#53;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"55\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49129fa7ef75154d92467c1a00c354f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#52;&#123;&#100;&#125;&#94;&#123;&#54;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df863f7de0d91ca09e5f4e8b69b62a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#123;&#117;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#50;&#123;&#118;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d9afe6a81a35f11af02ba7fda7476f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#123;&#107;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"58\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b60076a785fba8c17f9c239b5b39d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#123;&#106;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#106;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"55\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f2d60bad02c3cf9479dbf28ad0f6b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"65\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73d78c6daf8feb0121247485cc045df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"68\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ed9d7dece7bc142bb581c5d6072a06ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"93\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-273619ad7f2e84e63fd23c907dbeb121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#107;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"95\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b65afbd7251abe14c2102eef9ea20e94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"104\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa46a41f00ffdeafe263c1b62873e3ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#110;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"103\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596397707\">Divide Monomials<\/h2>\n<p id=\"fs-id1168745578183\">In the following exercises, divide the monomials.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa7e6ac9a78d84e3d388de557f03f11e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#92;&#100;&#105;&#118;&#32;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf778a74da459c5de484dab5ec6cfc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#51;&#123;&#118;&#125;&#94;&#123;&#49;&#48;&#125;&#92;&#100;&#105;&#118;&#32;&#57;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1506355d05879add87b6b9215a03464_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#56;&#123;&#121;&#125;&#94;&#123;&#49;&#53;&#125;&#92;&#100;&#105;&#118;&#32;&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de9783375b02523032d041801fecc03a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#50;&#123;&#117;&#125;&#94;&#123;&#49;&#50;&#125;&#92;&#100;&#105;&#118;&#32;&#49;&#50;&#123;&#117;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-211c82382f57dda9e230f4f80ef3c5c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#45;&#49;&#53;&#123;&#97;&#125;&#94;&#123;&#49;&#48;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -8px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e94997cd3ee44ac61639e870c9d5ba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#52;&#123;&#120;&#125;&#94;&#123;&#57;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#45;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"59\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64576929427d06ec433c64458d517e1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#123;&#114;&#125;&#94;&#123;&#52;&#125;&#123;&#115;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#49;&#56;&#123;&#114;&#125;&#94;&#123;&#57;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"41\" style=\"vertical-align: -8px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8952dd471db59837088336f6ecab0c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#51;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca9873a929cc9db09b84be6deccbbc96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#45;&#50;&#55;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"52\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5cb820fe485b809ecfb668dac17a2120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#45;&#54;&#48;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"53\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a53a89dfbfc2516778543228f19b7c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#52;&#123;&#113;&#125;&#94;&#123;&#49;&#49;&#125;&#123;&#114;&#125;&#94;&#123;&#57;&#125;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#52;&#56;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#123;&#114;&#125;&#94;&#123;&#56;&#125;&#123;&#115;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"60\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9139181b47da6daea1eaf509e55a1f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#123;&#97;&#125;&#94;&#123;&#49;&#48;&#125;&#123;&#98;&#125;&#94;&#123;&#56;&#125;&#123;&#99;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#52;&#50;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#123;&#98;&#125;&#94;&#123;&#54;&#125;&#123;&#99;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"60\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19356fdfe33ebf5af7dfdac3baabfdf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"31\" width=\"117\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ffbbd87d5f996fed174490c8edc2782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#123;&#113;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#45;&#51;&#54;&#123;&#112;&#125;&#94;&#123;&#49;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"124\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6e29c843a8ffac88951ea8ef6978a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#97;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"88\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1748952ead0200f746778afe3520b5a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#52;&#125;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"99\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596410134\">Mixed Practice<\/h2>\n<div id=\"fs-id1169596410140\" data-type=\"exercise\">\n<div id=\"fs-id1169596410142\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 313px;\">\n<tbody>\n<tr style=\"height: 139px;\">\n<td style=\"width: 50%; height: 139px;\">\n<div id=\"fs-id1169596410140\" data-type=\"exercise\">\n<div id=\"fs-id1169596410142\" data-type=\"problem\">\n<p id=\"fs-id1169596410144\">67.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b1361badf79e5a667e634366a9d1a8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#43;&#50;&#123;&#97;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"81\" style=\"vertical-align: -2px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9289820ea9e8f23870efff665b9be26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#45;&#50;&#123;&#97;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0de8e8234768e6d643791ed02fe2f622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#92;&#100;&#111;&#116;&#32;&#50;&#123;&#97;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61d74ef485dc083923fc84da3e4c256a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#92;&#100;&#105;&#118;&#32;&#50;&#123;&#97;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596410270\" data-type=\"exercise\">\n<div id=\"fs-id1169596410272\" data-type=\"problem\">\n<p id=\"fs-id1169596410274\">\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 50%; height: 139px;\">\n<p id=\"fs-id1169596363438\">69.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e57b26bf3ec1c28494a83d4e475d4d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#112;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75f19c5cedee7bab3674ecabc41739e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596382448\">70.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24938385d3cfa5944b42e5b525c6f878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"45\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8286b828710c8003c6209486de959e00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"37\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169596382516\">71.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c625c8ec03340a629417c92214efe885_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"15\" style=\"vertical-align: -9px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3504aac18823dca2e9b0c9d922b16f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"15\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169596382577\">72.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8804930b08b3249924249035e4bf720e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#122;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"14\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1b487ba8205e99e7ae2191836e4a394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">73.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-549a03712d891b5982db365c08224d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"124\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2c5c0bb18b87395be7e825834ee7b65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-354ec73c265be2175a9c3a49d1d92aa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#51;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#52;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#57;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"81\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2cbc9a8026751608adf654b4ab9c664a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#50;&#123;&#99;&#125;&#94;&#123;&#49;&#49;&#125;&#125;&#123;&#52;&#123;&#99;&#125;&#94;&#123;&#53;&#125;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#123;&#99;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#54;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"85\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8bd8df16a1d85f2aa2132ec398964e2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#50;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"87\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32786ae68c7a99f42bbcb96fda073e8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#54;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#53;&#123;&#120;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#55;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"83\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a69f66db683e562c3eea9e4db778e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#51;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#57;&#123;&#114;&#125;&#94;&#123;&#52;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#50;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#54;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"107\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-776924f44fed0439b469fad3c3f7076f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#53;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"109\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">81.<strong data-effect=\"bold\"> Memory<\/strong> One megabyte is approximately <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bde83e3acac1b7752d5d12b89c9ad11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> bytes. One gigabyte is approximately <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f61dad5c0eb8b555da26ab7075efd472_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> bytes. How many megabytes are in one gigabyte?<\/td>\n<td style=\"width: 50%;\">82.<strong data-effect=\"bold\"> Memory<\/strong> One gigabyte is approximately <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f61dad5c0eb8b555da26ab7075efd472_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> bytes. One terabyte is approximately <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32d90708336207fbf3c306879a79ae3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/> bytes. How many gigabytes are in one terabyte?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">83. Jennifer thinks the quotient <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7bda75125a24267e2d244230748378b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#50;&#52;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"20\" style=\"vertical-align: -7px;\" \/> simplifies to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-338254cc06a4a74a0fe2e45945acf0d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>. What is wrong with her reasoning?<\/td>\n<td style=\"width: 50%;\">84. Maurice simplifies the quotient <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e2aa48719293299a70036e02b4beecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#100;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"14\" style=\"vertical-align: -6px;\" \/> by writing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c5254dcaeff2c67b0e3e38c0ac28806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#100;&#125;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#100;&#125;&#125;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"54\" style=\"vertical-align: -12px;\" \/>. What is wrong with his reasoning?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">85. When Drake simplified <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c262bace6a55446d8f6d8f8b21b2a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a8f270ab874929b4b7845f6efc443f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> he got the same answer. Explain how using the Order of Operations correctly gives different answers.<\/td>\n<td style=\"width: 50%;\">86. Robert thinks <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95e1fbd22322e50026adf320eb6007ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> simplifies to 0. What would you say to convince Robert he is wrong?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 196px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">2. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18f0c771be0f5f7f94a86466c8873ac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9e049a05cbf2a4362f0876986f6685c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">4. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-179e14cb43583e8e04eb9e779a65209d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68ebe56b1a3fb43464f27ba3fd0b4f6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">6. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f325179b479d178d7e99b8090ec073f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#116;&#125;&#94;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"18\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb706af686b17e6e2ed0e8bfa7594950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">8. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1aba8c728467c5a671985d62c0a8d3cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"15\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82c692fc7c77d012d64039079d9df525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">10. a) 1 b) 1<\/td>\n<td style=\"width: 50%; height: 16px;\">12. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">14. a) 1 b) 6<\/td>\n<td style=\"width: 50%; height: 16px;\">16. a) 7 b) 1<\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 50%; height: 34px;\">18. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 0<\/td>\n<td style=\"width: 50%; height: 34px;\">20. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f27b1929b4e6c3e5a8f36ab7480700b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1159634fba55d60f1c1d30e1e12d5e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#56;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"15\" style=\"vertical-align: -7px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dd4a957c14cf0369a1489f57cd6ce22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 50%; height: 34px;\">22. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95ad9dfca47e9ab0354afcb8e849e262_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"21\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c0f3f062963cdf5e458c8a8aa0ec57b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#44;&#48;&#48;&#48;&#125;&#123;&#56;&#49;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"39\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 34px;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a4f8615b90278cca9039384576017d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48541f82788d9b97a870606bd6257cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">28. 1<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-761bb9f403cd90813174f7e7e4b2aabe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"22\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0839d4ce7e7ca5a45f2010fe4614e545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-461895b5185960ac31f9865782409d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"25\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">36.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-909d33cc61b8ce98a968908ac86d7637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#49;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"19\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c6d2aa7ae6b1e092172ecedf30d86ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#48;&#125;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#53;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6aa4ab57fc064b9614ed2e5932a3708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#109;&#125;&#94;&#123;&#49;&#53;&#125;&#125;&#123;&#49;&#50;&#53;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"39\" style=\"vertical-align: -8px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f896ef182e5bf8495446f560287fba54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#50;&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#56;&#125;&#125;&#123;&#49;&#54;&#123;&#118;&#125;&#94;&#123;&#123;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"42\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3c0f994de3b7eb2f956210d68282f24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#106;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ac5897ba96c574750d6f75c286c4308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"14\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38221c79a800ac56a8b2e6766c9f06b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#123;&#107;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ccf3155c199df3f0292e40c24695e91b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d588ddfbd20266e4055f55896d55a69d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#118;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c2905b0934ac6679b71bd02be32e44c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#117;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fdbc39ce3668a139a3b72a8cc61c78cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"37\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-413b821ede51c3c8c2018727545d1f64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"37\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9bf2ae31c43a377048abf28d3c8b487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a48cc451c7874c5b2dab0c3a5e827b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#52;&#50;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"41\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfc011a5350d8bb402a7d7cbebd7f48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"31\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec50c7ee0563a9bdbc0f75ab8ba0b31e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">68.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30ead3e1ad605ed583d27f4f8726bb1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#123;&#110;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3ab079b20dd23e4ab8fc24c27bb844b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#110;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d5b709bd164068865a6a977ff7cdcac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#123;&#110;&#125;&#94;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/><br \/>\nd) 5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">70.<\/p>\n<div id=\"fs-id1169596382444\" data-type=\"exercise\">\n<div id=\"fs-id1169596382487\" data-type=\"solution\">\n<p id=\"fs-id1169596382489\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5cf1a965a41c95735140625d09cefd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc867730daa2f7fcf6dc36a505257f08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 50%;\">72. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2334b510e059b51ec659ad92b105d05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#122;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84c0ed0d227dbeb130eba5b05d846cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5857dc4ae43dc840aea47552bffd6a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#99;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"32\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9608403b176cb023606ca01493d9f883_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56c1aff9ef303cbaa2510b7c33fed889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1bae90f4f176715204f5d606849580b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">84. Answers will vary.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">86. Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cDivide Monomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n","protected":false},"author":90,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1972","chapter","type-chapter","status-publish","hentry"],"part":1897,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1972\/revisions"}],"predecessor-version":[{"id":1973,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1972\/revisions\/1973"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/1897"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1972\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1972"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1972"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1972"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}