{"id":1940,"date":"2020-08-21T19:41:50","date_gmt":"2020-08-21T23:41:50","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-multiplication-properties-of-exponents\/"},"modified":"2025-09-16T14:25:40","modified_gmt":"2025-09-16T18:25:40","slug":"use-multiplication-properties-of-exponents","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-multiplication-properties-of-exponents\/","title":{"raw":"7.1 Use Multiplication Properties of Exponents","rendered":"7.1 Use Multiplication Properties 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 with exponents<\/li>\n \t<li>Simplify expressions using the Product Property for Exponents<\/li>\n \t<li>Simplify expressions using the Power Property for Exponents<\/li>\n \t<li>Simplify expressions using the Product to a Power Property<\/li>\n \t<li>Simplify expressions by applying several properties<\/li>\n \t<li>Multiply monomials<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Simplify Expressions with Exponents<\/h1>\n<p id=\"fs-id1169597499873\">Remember that an exponent indicates repeated multiplication of the same quantity. For example, \\({2}^{4}\\) means to multiply 2 by itself 4 times, so \\({2}^{4}\\) means 2 \u00b7 2 \u00b7 2 \u00b7 2<\/p>\n<p id=\"fs-id1169597431995\">Let\u2019s review the vocabulary for expressions with exponents.<\/p>\n\n<div id=\"fs-id1169597500173\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Exponential Notation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n<span id=\"fs-id1169597508648\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m power means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_02_001_img_new.jpg\" alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m power means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597488943\">This is read \\(a\\) to the \\({m}^{th}\\) power.<\/p>\n<p id=\"fs-id1169597464781\">In the expression \\({a}^{m}\\), the <em data-effect=\"italics\">exponent<\/em> \\(m\\) tells us how many times we use the <em data-effect=\"italics\">base<\/em> \\(a\\) as a factor.<\/p>\n<span id=\"fs-id1169597420838\" data-type=\"media\" data-alt=\"This figure has two columns. The left column contains 4 cubed. Below this is 4 times 4 times 4, with \u201c3 factors\u201d written below in blue. The right column contains negative 9 to the fifth power. Below this is negative 9 times negative 9 times negative 9 times negative 9 times negative 9, with \u201c5 factors\u201d written below in blue.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_002_img_new.jpg\" alt=\"This figure has two columns. The left column contains 4 cubed. Below this is 4 times 4 times 4, with \u201c3 factors\u201d written below in blue. The right column contains negative 9 to the fifth power. Below this is negative 9 times negative 9 times negative 9 times negative 9 times negative 9, with \u201c5 factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1169597357034\">Before we begin working with variable expressions containing exponents, let\u2019s simplify a few expressions involving only numbers.<\/p>\n\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-id1169597464503\" data-type=\"problem\">\n<p id=\"fs-id1169597517035\">Simplify: a) \\({4}^{3}\\) b) \\({7}^{1}\\) c) \\({\\left(\\dfrac{5}{6}\\right)}^{2}\\) d) \\({\\left(0.63\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597379020\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-50\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td>\\({4}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply three factors of 4.<\/td>\n<td>4 \u00b7 4 \u00b7 4<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(64\\)<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\({7}^{1}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply one factor of 7.<\/td>\n<td>\\(7\\)<\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td>\\({\\left(\\dfrac{5}{6}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td>\\(\\left(\\dfrac{5}{6}\\right)\\left(\\dfrac{5}{6}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(\\dfrac{25}{36}\\)<\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td>\\({\\left(0.63\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td>\\(\\left(0.63\\right)\\left(0.63\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(0.3969\\)<\/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 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597491698\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597497979\" data-type=\"exercise\">\n<div id=\"fs-id1169597446527\" data-type=\"problem\">\n<p id=\"fs-id1169597395263\">Simplify: a) \\({6}^{3}\\) b) \\({15}^{1}\\) c) \\({\\left(\\dfrac{3}{7}\\right)}^{2}\\) d) \\({\\left(0.43\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597342610\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597367714\">a) 216 b) \\(15\\) c) \\(\\dfrac{9}{49}\\) d) 0.1849<\/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-id1169597420581\" data-type=\"problem\">\n<p id=\"fs-id1169597467163\">Simplify: a) \\({2}^{5}\\) b) \\({21}^{1}\\) c) \\({\\left(\\dfrac{2}{5}\\right)}^{3}\\) d) \\({\\left(0.218\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597532637\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597420188\">a) \\(32\\)b) 21 c) \\(\\dfrac{8}{125}\\) d) \\(0.047524\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597406059\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597531640\" data-type=\"exercise\">\n<div id=\"fs-id1169597532637\" 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-id1169597411906\" data-type=\"problem\">\n<p id=\"fs-id1169597497879\">Simplify: a) \\({\\left(-5\\right)}^{4}\\) b) \\(-{5}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597493725\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-539\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td>\\({\\left(-5\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply four factors of \\(-5\\).<\/td>\n<td>\\(\\left(-5\\right)\\left(-5\\right)\\left(-5\\right)\\left(-5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(625\\)<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\(-{5}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply four factors of 5.<\/td>\n<td>-(5\u00a0 \u00b7 5 \u00b7 5 \u00b7 5)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(-625\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597444745\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\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-id1169597444745\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\n<p id=\"fs-id1169597415505\">Simplify: a) \\({\\left(-3\\right)}^{4}\\) b) \\(-{3}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597495810\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597537923\">a) \\(81\\) b) \\(-81\\)<\/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 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597340444\" data-type=\"problem\">\n<p id=\"fs-id1169597447205\">Simplify: a) \\({\\left(-13\\right)}^{2}\\) b) \\(-{13}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597351946\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597406596\">a) \\(169\\) b) \\(-169\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597448020\">Notice the similarities and differences in <a class=\"autogenerated-content\" href=\"#fs-id1169597411906\">(Example 2)<\/a> a) and <a class=\"autogenerated-content\" href=\"#fs-id1169597411906\">(Example 2)<\/a> b)! Why are the answers different? As we follow the order of operations in part a) the parentheses tell us to raise the \\(\\left(-5\\right)\\) to the 4<sup>th<\/sup> power. In part b) we raise just the 5 to the 4<sup>th<\/sup> power and then take the opposite.<\/p>\n\n<h1 data-type=\"title\">Simplify Expressions Using the Product Property for Exponents<\/h1>\n<p id=\"fs-id1169597350867\">You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too.<\/p>\n<p id=\"fs-id1169597501890\">We\u2019ll derive the properties of exponents by looking for patterns in several examples.<\/p>\n<p id=\"fs-id1169597408681\">First, we will look at an example that leads to the Product Property.<\/p>\n\n<table id=\"eip-id1172187661170\" class=\"grid\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the text in the left column says \u201cWhat does this mean?\u201d In the right column is x squared times x cubed. One row down, the text in the left column says \u201cHow many factors altogether?\u201d In the right column is x times x, times x times x times x. \u201c2 factors\u201d is written below x times x and \u201c3 factors\u201d is written below x times x times x. Below this is a bracket, beneath which \u201c5 factors\u201d is written in blue. One row down, the text in the left column says \u201cSo we have\u201d. In the right column is x to the fifth power. One row down, the text in the left column says \u201cNotice that 5 is the sum of the exponents, 2 and 3.\u201d In the right column is the text \u201cx squared times x cubed is x to the 2 plus 3 power, or x to the fifth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187661190\" data-type=\"media\" data-alt=\"x squared times x cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003a_img_new.jpg\" alt=\"x squared times x cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">What does this mean?\nHow many factors altogether?<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1172187661215\" data-type=\"media\" data-alt=\"x times x, multiplied by x times x. x times x has two factors. x times x times x has three factors. 2 plus 3 is five factors.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003b_img_new.jpg\" alt=\"x times x, multiplied by x times x. x times x has two factors. x times x times x has three factors. 2 plus 3 is five factors.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>So, we have<\/td>\n<td data-align=\"left\"><span id=\"eip-id1172187661234\" data-type=\"media\" data-alt=\"x to the fifth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003c_img_new.jpg\" alt=\"x to the fifth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice that 5 is the sum of the exponents, 2 and 3.<\/td>\n<td><span id=\"eip-id1172187661250\" data-type=\"media\" data-alt=\"x squared times x cubed is x to the power of 2 plus 3, or x to the fifth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003d_img_new.jpg\" alt=\"x squared times x cubed is x to the power of 2 plus 3, or x to the fifth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597334107\">We write:<\/p>\n\n<div id=\"fs-id1169597498272\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c} {x}^{2}\\cdot {x}^{3} \\\\\u00a0 {x}^{2+3} \\\\\u00a0 {x}^{5} \\end{array}\\)<\/div>\n<p id=\"fs-id1169597430306\">The base stayed the same and we added the exponents. This leads to the <strong data-effect=\"bold\">Product Property for Exponents<\/strong>.<\/p>\n\n<div id=\"fs-id1169597397855\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Product Property for Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597491806\">If \\(a\\) is a real number, and \\(m\\) and \\(n\\) are counting numbers, then<\/p>\n\n<div id=\"fs-id1169597359735\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({a}^{m}\\cdot {a}^{n}={a}^{m+n}\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597397229\">To multiply with like bases, add the exponents.<\/p>\n\n<\/div>\n<p id=\"fs-id1169597410476\">An example with numbers helps to verify this property.<\/p>\n\n<div id=\"fs-id1169597490292\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{rcl} {2}^{2}\\cdot {2}^{3}&amp; \\stackrel{?}{=} &amp; {2}^{2+3} \\\\\u00a0 4\\cdot 8 &amp; \\stackrel{?}{=} &amp; {2}^{5}\\hfill \\\\ 32&amp; = &amp; 32\\checkmark \\hfill \\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 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597484664\" data-type=\"problem\">\n<p id=\"fs-id1169597441330\">Simplify: \\({y}^{5}\\cdot {y}^{6}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597479966\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172188903486\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains y to the fifth power times y to the sixth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is y to the 5 plus 6 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is y to the eleventh power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172188903506\" data-type=\"media\" data-alt=\"y to the fifth power times y to the sixth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004a_img_new.jpg\" alt=\"y to the fifth power times y to the sixth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \\cdot <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172188903523\" data-type=\"media\" data-alt=\"y to the power of 5 plus 6.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004b_img_new.jpg\" alt=\"y to the power of 5 plus 6.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172188903539\" data-type=\"media\" data-alt=\"y to the eleventh power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004c_img_new.jpg\" alt=\"y to the eleventh power.\" 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 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576688\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597478796\" data-type=\"exercise\">\n<div id=\"fs-id1169597419943\" data-type=\"problem\">\n<p id=\"fs-id1169597538332\">Simplify: \\({b}^{9}\\cdot {b}^{8}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597536170\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597490790\">\\({b}^{17}\\)<\/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-id1169597502452\" data-type=\"problem\">\n<p id=\"fs-id1169597410315\">Simplify: \\({x}^{12}\\cdot {x}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597376680\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597528228\">\\({x}^{16}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597495832\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597504597\" data-type=\"exercise\">\n<div id=\"fs-id1169597376680\" data-type=\"solution\">\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-id1169597397528\" data-type=\"problem\">\n<p id=\"fs-id1169597497488\">Simplify: a) \\({2}^{5}\\cdot {2}^{9}\\) b) \\(3\\cdot {3}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597459920\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745220462\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1172187839283\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 2 to the fifth power times 2 to the ninth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is 2 to the 5 plus 9 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 2 to the fourteenth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187839303\" data-type=\"media\" data-alt=\"2 to the fifth power times 2 to the ninth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005a_img_new.jpg\" alt=\"2 to the fifth power times 2 to the ninth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187839328\" data-type=\"media\" data-alt=\"2 to the power of 5 plus 9.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005b_img_new.jpg\" alt=\"2 to the power of 5 plus 9.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187990102\" data-type=\"media\" data-alt=\"2 to the 14th power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005c_img_new.jpg\" alt=\"2 to the 14th power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>\n<table id=\"eip-id1172187678535\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 3 times 3 to the fourth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is 3 to the 1 plus 4 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 3 to the fifth power\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187678555\" data-type=\"media\" data-alt=\"3 to the fifth power times 3 to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006a_img_new.jpg\" alt=\"3 to the fifth power times 3 to the fourth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187678580\" data-type=\"media\" data-alt=\"3 to the power of 5 plus 4.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006b_img_new.jpg\" alt=\"3 to the power of 5 plus 4.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187678597\" data-type=\"media\" data-alt=\"3 to the ninth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006c_img_new.jpg\" alt=\"3 to the ninth 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 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597392408\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597432293\" data-type=\"exercise\">\n<div id=\"fs-id1169597523718\" data-type=\"problem\">\n<p id=\"fs-id1169597527464\">Simplify: a) \\(5\\cdot {5}^{5}\\) b) \\({4}^{9}\\cdot {4}^{9}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597339458\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597389559\">a) \\({5}^{6}\\) b) \\({4}^{18}\\)<\/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-id1169597539933\" data-type=\"problem\">\n<p id=\"fs-id1169597400959\">Simplify: a) \\({7}^{6}\\cdot {7}^{8}\\) b) \\(10\\cdot {10}^{10}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597485232\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597397173\">a) \\({7}^{14}\\) b) \\({10}^{11}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597445862\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597526418\" data-type=\"exercise\">\n<div id=\"fs-id1169597485232\" data-type=\"solution\">\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-id1169597506773\" data-type=\"problem\">\n<p id=\"fs-id1169597447809\">Simplify: a) \\({a}^{7}\\cdot a\\) b) \\({x}^{27}\\cdot {x}^{13}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597481014\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745203075\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1172182437179\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains a to the seventh power times a. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is a to the 7 plus 1 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is a to the eighth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182437199\" data-type=\"media\" data-alt=\"a to the seventh power times a.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007a_img_new.jpg\" alt=\"a to the seventh power times a.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite, a = a<sup>1<\/sup>.<\/td>\n<td><span id=\"eip-id1172182372263\" data-type=\"media\" data-alt=\"a to the seventh power times a to the first power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007b_img_new.jpg\" alt=\"a to the seventh power times a to the first power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172182372288\" data-type=\"media\" data-alt=\"a to the power of 7 plus 1.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007c_img_new.jpg\" alt=\"a to the power of 7 plus 1.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182372304\" data-type=\"media\" data-alt=\"a to the eighth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007d_img_new.jpg\" alt=\"a to the eighth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>\n<table id=\"eip-id1172187957456\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains x to the twenty seventh power times x to the thirteenth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is x to the 27 plus 13 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is x to the fortieth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187957476\" data-type=\"media\" data-alt=\"x to the twenty-seventh power times x to the thirteenth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008a_img_new.jpg\" alt=\"x to the twenty-seventh power times x to the thirteenth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice, the bases are the same, so add the exponents.<\/td>\n<td><span id=\"eip-id1172187957493\" data-type=\"media\" data-alt=\"x to the power of 27 plus 13.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008b_img_new.jpg\" alt=\"x to the power of 27 plus 13.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187957510\" data-type=\"media\" data-alt=\"x to the fortieth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008c_img_new.jpg\" alt=\"x to the fortieth 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 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597502123\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597498478\" data-type=\"exercise\">\n<div id=\"fs-id1169597525992\" data-type=\"problem\">\n<p id=\"fs-id1169597517413\">Simplify: a) \\({p}^{5}\\cdot p\\) b) \\({y}^{14}\\cdot {y}^{29}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597530042\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597535102\">a) \\({p}^{6}\\) b) \\({y}^{43}\\)<\/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 id=\"fs-id1169597690271\" data-type=\"problem\">\n<p id=\"fs-id1169597690273\">Simplify: a) \\(z\\cdot {z}^{7}\\) b) \\({b}^{15}\\cdot {b}^{34}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597396891\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597460764\">a) \\({z}^{8}\\) b) \\({b}^{49}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597689405\">We can extend the Product Property for Exponents to more than two factors.<\/p>\n\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-id1169597479150\" data-type=\"problem\">\n<p id=\"fs-id1169597492751\">Simplify: \\({d}^{4}\\cdot {d}^{5}\\cdot {d}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597691555\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187986203\" class=\"unnumbered unstyled\" style=\"height: 45px;\" summary=\"This figure has two columns. At the top of the figure, the right column contains d to the fourth power times d to the fifth power times d squared. One row down, the left column says \u201cAdd the exponents, since bases are the same.\u201d In the right column is d to the 4 plus 5 plus 2 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is d to the eleventh power.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\"><\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986223\" data-type=\"media\" data-alt=\"d to the fourth power times d to the fifth power times d squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009a_img_new.jpg\" alt=\"d to the fourth power times d to the fifth power times d squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\">Add the exponents, since bases are the same.<\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986240\" data-type=\"media\" data-alt=\"d to the power of 4 plus 5 plus 2.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009b_img_new.jpg\" alt=\"d to the power of 4 plus 5 plus 2.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986258\" data-type=\"media\" data-alt=\"d to the eleventh power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009c_img_new.jpg\" alt=\"d to the eleventh power.\" 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<div id=\"fs-id1169597466455\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597466458\" data-type=\"exercise\">\n<div id=\"fs-id1169597484498\" data-type=\"problem\">\n<p id=\"fs-id1169597484501\">Simplify: \\({x}^{6}\\cdot {x}^{4}\\cdot {x}^{8}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597508776\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597508778\">\\({x}^{18}\\)<\/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 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597500442\" data-type=\"problem\">\n<p id=\"fs-id1169597500445\">Simplify: \\({b}^{5}\\cdot {b}^{9}\\cdot {b}^{5}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597577193\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597517090\">\\({b}^{19}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Power Property for Exponents<\/h1>\n<p id=\"fs-id1169597461953\">Now let\u2019s look at an exponential expression that contains a power raised to a power. See if you can discover a general property.<\/p>\n\n<table id=\"eip-id1172188999640\" class=\"grid\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the right column contains x squared, in parentheses, cubed. One row down, the text in the left column says \u201cWhat does this mean?\u201d In the right column is x squared times x squared times x squared. One row down, the text in the left column says \u201cHow many factors altogether?\u201d In the right column is x times x, times x times x, times x times x. \u201c2 factors\u201d is written below each of the three instances of x times x. Below this is a bracket, beneath which \u201c6 factors\u201d is written in blue. One row down, the text in the left column says \u201cSo we have\u201d. In the right column is x to the sixth power. One row down, the text in the left column says \u201cNotice that 6 is the product of the exponents, 2 and 3.\u201d In the right column is \u201cx squared, in parentheses, cubed, is x to the 2 times 3 power, or x to the sixth power.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172188999660\" data-type=\"media\" data-alt=\"x squared, in parentheses, cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010a_img_new.jpg\" alt=\"x squared, in parentheses, cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">What does this mean?\nHow many factors altogether?<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1172188999686\" data-type=\"media\" data-alt=\"x squared cubed is x squared times x squared times x squared, which is x times x, multiplied by x times x, multiplied by x times x. x times x has two factors. Two plus two plus two is six factors.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010b_img_new.jpg\" alt=\"x squared cubed is x squared times x squared times x squared, which is x times x, multiplied by x times x, multiplied by x times x. x times x has two factors. Two plus two plus two is six factors.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>So we have<\/td>\n<td><span id=\"eip-id1172188999702\" data-type=\"media\" data-alt=\"x to the sixth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010c_img_new.jpg\" alt=\"x to the sixth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice that 6 is the product of the exponents, 2 and 3.<\/td>\n<td><span id=\"eip-id1172188999719\" data-type=\"media\" data-alt=\"x squared cubed is x to the power of 2 times 3, or x to the sixth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010d_img_new.jpg\" alt=\"x squared cubed is x to the power of 2 times 3, or x to the sixth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597422219\">We write:<\/p>\n\n<div id=\"fs-id1169597533352\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c} {\\left({x}^{2}\\right)}^{3} \\\\ {x}^{2\\cdot 3} \\\\\u00a0 {x}^{6} \\end{array}\\)<\/div>\n<p id=\"fs-id1169597537342\">We multiplied the exponents. This leads to the Power Property for Exponents.<\/p>\n\n<div id=\"fs-id1169597577174\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Power Property for Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597467027\">If \\(a\\) is a real number, and \\(m\\) and \\(n\\) are whole numbers, then<\/p>\n\\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\)\n\n<\/div>\n<\/div>\nTo raise a power to a power, multiply the exponents.\n\n<\/div>\n<\/div>\n<p id=\"fs-id1169597537099\">An example with numbers helps to verify this property.<\/p>\n\n<div id=\"fs-id1169597464874\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{rcl} {2}^{2}\\cdot {2}^{3}&amp; \\stackrel{?}{=} &amp; {2}^{2+3} \\\\\u00a0 4\\cdot 8 &amp; \\stackrel{?}{=} &amp; {2}^{5} \\\\ 32&amp; = &amp; 32\\checkmark \\hfill \\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 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597518560\" data-type=\"problem\">\n<p id=\"fs-id1169597690624\">Simplify: a) \\({\\left({y}^{5}\\right)}^{9}\\) b) \\({\\left({4}^{4}\\right)}^{7}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597480454\" 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-id1166425254840\">a)<\/p>\n\n<table id=\"eip-id1172186692197\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains y to the fifth power, in parentheses, to the ninth power. One row down, the left column says \u201cUse the power property, a to the m power, in parentheses, to the n power equals a to the m times n power.\u201d In the right column is y to the 5 times 9 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is y to the forty-fifth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172186692218\" data-type=\"media\" data-alt=\"y to the fifth power, in parentheses, to the ninth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011a_img_new.jpg\" alt=\"y to the fifth power, in parentheses, to the ninth power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the power property, (<em data-effect=\"italics\">a<sup>m<\/sup><\/em>)<em data-effect=\"italics\"><sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m \u00b7 n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172186692244\" data-type=\"media\" data-alt=\"y to the power of 5 times 9.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011b_img_new.jpg\" alt=\"y to the power of 5 times 9.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186692261\" data-type=\"media\" data-alt=\"y to the 45th power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011c_img_new.jpg\" alt=\"y to the 45th power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nb)\n<table id=\"eip-id1172187801343\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 4 to the fourth power, in parentheses, to the seventh power. One row down, the left column says \u201cUse the power property, a to the m power, in parentheses, to the n power equals a to the m times n power.\u201d In the right column is 4 to the 4 times 7 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 4 to the twenty-eighth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187801363\" data-type=\"media\" data-alt=\"4 to the fourth power, in parentheses, to the 7th power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012a_img_new.jpg\" alt=\"4 to the fourth power, in parentheses, to the 7th power.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the power property.<\/td>\n<td><span id=\"eip-id1172187801380\" data-type=\"media\" data-alt=\"4 to the power of 4 times 7.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012b_img_new.jpg\" alt=\"4 to the power of 4 times 7.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187801396\" data-type=\"media\" data-alt=\"4 to the twenty-eighth power.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012c_img_new.jpg\" alt=\"4 to the twenty-eighth power.\" 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 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597515984\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597515987\" data-type=\"exercise\">\n<div id=\"fs-id1169597691563\" data-type=\"problem\">\n<p id=\"fs-id1169597691565\">Simplify: a) \\({\\left({b}^{7}\\right)}^{5}\\) b) \\({\\left({5}^{4}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597577234\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597505931\">a) \\({b}^{35}\\) b) \\({5}^{12}\\)<\/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-id1169597508068\" data-type=\"problem\">\n<p id=\"fs-id1169597530485\">Simplify: a) \\({\\left({z}^{6}\\right)}^{9}\\) b) \\({\\left({3}^{7}\\right)}^{7}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597521282\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597538336\">a) \\({z}^{54}\\) b) \\({3}^{49}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Product to a Power Property<\/h1>\n<p id=\"fs-id1169597579504\">We will now look at an expression containing a product that is raised to a power. Can you find this pattern?<\/p>\n\n<table id=\"eip-416\" class=\"grid\" style=\"width: 100%;\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\({\\left(2x\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>What does this mean?<\/td>\n<td>\\(2x\\cdot 2x\\cdot 2x\\)<\/td>\n<\/tr>\n<tr>\n<td>We group the like factors together.<\/td>\n<td>\\(2\\cdot 2 \\cdot 2 \\cdot x \\cdot x \\cdot x\\)<\/td>\n<\/tr>\n<tr>\n<td>How many factors of 2 and of \\(x\\)?<\/td>\n<td>\\({2}^{3}\\cdot {x}^{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597540864\">Notice that each factor was raised to the power and \\({\\left(2x\\right)}^{3}\\) is \\({2}^{3}\\cdot {x}^{3}\\).<\/p>\n\n<table id=\"eip-300\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>We write:<\/td>\n<td>\\({\\left(2x\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\({2}^{3}\\cdot {x}^{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597577372\">The exponent applies to each of the factors! This leads to the Product to a Power Property for Exponents.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Product to a Power Property for Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597542287\">If \\(a\\) and \\(b\\) are real numbers and \\(m\\) is a whole number, then<\/p>\n\\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\)\n\nTo raise a product to a power, raise each factor to that power.\n\n<\/div>\n<\/div>\n<p id=\"fs-id1169597688061\">An example with numbers helps to verify this property:<\/p>\n\\(\\begin{array}{rcl} {\\left(2\\cdot 3\\right)}^{2}&amp; \\stackrel{?}{=} &amp; {2}^{2}\\cdot {3}^{2} \\\\\u00a0 {6}^{2}&amp; \\stackrel{?}{=} &amp; 4\\cdot 9 \\\\\u00a0 36&amp; = &amp; 36\\checkmark \\end{array}\\)\n<div data-type=\"equation\" data-label=\"\">\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-id1169597541988\" data-type=\"problem\">\n<p id=\"fs-id1169597541990\">Simplify: a) \\({\\left(-9d\\right)}^{2}\\) b) \\({\\left(3mn\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597448611\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745206751\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1172182438507\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains negative 9d squared. One row down, the left column says \u201cUse Power of a Product Property, ab to the m power equals a to the m power b to the m power.\u201d In the right column is negative 9 squared d squared. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 81d squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182437006\" data-type=\"media\" data-alt=\"Negative 9 d squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013a_img_new.jpg\" alt=\"Negative 9 d squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use Power of a Product Property, (<em data-effect=\"italics\">ab<\/em>)<em data-effect=\"italics\"><sup>m<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m<\/sup>b<sup>m<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172182437032\" data-type=\"media\" data-alt=\"negative 9 squared d squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013b_img_new.jpg\" alt=\"negative 9 squared d squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182437048\" data-type=\"media\" data-alt=\"81 d squared.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013c_img_new.jpg\" alt=\"81 d squared.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t<li>\n<table id=\"eip-id1172187986280\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 3mn cubed. One row down, the left column says \u201cUse Power of a Product Property, ab to the m power equals a to the m power b to the m power.\u201d In the right column is 3 cubed m cubed n cubed. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 27m cubed n cubed.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187986300\" data-type=\"media\" data-alt=\"3 m n cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014a_img_new.jpg\" alt=\"3 m n cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use Power of a Product Property, (<em data-effect=\"italics\">ab<\/em>)<em data-effect=\"italics\"><sup>m<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m<\/sup>b<sup>m<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187986327\" data-type=\"media\" data-alt=\"3 cubed m cubed n cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014b_img_new.jpg\" alt=\"3 cubed m cubed n cubed.\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187986344\" data-type=\"media\" data-alt=\"27 m cubed n cubed.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014c_img_new.jpg\" alt=\"27 m cubed n cubed.\" 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 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597508854\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597508858\" data-type=\"exercise\">\n<div id=\"fs-id1169597538092\" data-type=\"problem\">\n<p id=\"fs-id1169597538094\">Simplify: a) \\({\\left(-12y\\right)}^{2}\\) b) \\({\\left(2wx\\right)}^{5}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597512464\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597512466\">a) \\(144{y}^{2}\\) b) \\(32{w}^{5}{x}^{5}\\)<\/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 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597460895\" data-type=\"problem\">\n<p id=\"fs-id1169597460897\">Simplify: a) \\({\\left(5wx\\right)}^{3}\\) b) \\({\\left(-3y\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597518878\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597518880\">a) \\(125{w}^{3}{x}^{3}\\) b) \\(-27{y}^{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Applying Several Properties<\/h1>\n<p id=\"fs-id1169597516917\">We now have three properties for multiplying expressions with exponents. Let\u2019s summarize them and then we\u2019ll do some examples that use more than one of the properties.<\/p>\n\n<div id=\"fs-id1169597538041\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597503103\">If \\(a\\) and \\(b\\) are real numbers, and \\(m\\) and \\(n\\) are whole numbers, then<\/p>\n\n<table id=\"eip-536\" 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>\\(({a}^{m})^{n} =\u00a0 {a}^{m \\cdot n}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Product to a Power<\/strong><\/td>\n<td>\\( (ab)^{m} = {a}^{m}{b}^{m}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nAll exponent properties hold true for any real numbers\\(m\\) and \\(n\\). Right now, we only use whole number exponents.\n\n<\/div>\n<\/div>\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 id=\"fs-id1169597466702\" data-type=\"problem\">\n<p id=\"fs-id1169597466704\">Simplify: a) \\({\\left({y}^{3}\\right)}^{6}{\\left({y}^{5}\\right)}^{4}\\) b) \\({\\left(-6{x}^{4}{y}^{5}\\right)}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597689335\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-886\" style=\"width: 100%;\" summary=\"\/\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td>\\({\\left({y}^{3}\\right)}^{6}{\\left({y}^{5}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>\\({y}^{18}\\cdot {y}^{20}\\)<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents.<\/td>\n<td>\\({y}^{38}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\({\\left(-6{x}^{4}{y}^{5}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property.<\/td>\n<td>\\({\\left(-6\\right)}^{2}{\\left({x}^{4}\\right)}^{2}{\\left({y}^{5}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>\\({\\left(-6\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(36{x}^{8}{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-id1169597516190\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597485072\" data-type=\"exercise\">\n<div id=\"fs-id1169597485074\" data-type=\"problem\">\n<p id=\"fs-id1169597485076\">Simplify: a) \\({\\left({a}^{4}\\right)}^{5}{\\left({a}^{7}\\right)}^{4}\\) b) \\({\\left(-2{c}^{4}{d}^{2}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597467471\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597467473\">a) \\({a}^{48}\\) b) \\(-8{c}^{12}{d}^{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 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597467696\" data-type=\"problem\">\n<p id=\"fs-id1169597467597\">Simplify: a) \\({\\left(-3{x}^{6}{y}^{7}\\right)}^{4}\\) b) \\({\\left({q}^{4}\\right)}^{5}{\\left({q}^{3}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597467809\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597467812\">a) \\(81{x}^{24}{y}^{28}\\) b) \\({q}^{29}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597467690\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597467694\" data-type=\"exercise\">\n<div id=\"fs-id1169597467809\" data-type=\"solution\">\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-id1169597467921\" data-type=\"problem\">\n<p id=\"fs-id1169597467923\">Simplify: a) \\({\\left(5m\\right)}^{2}\\left(3{m}^{3}\\right)\\) b) \\({\\left(3{x}^{2}y\\right)}^{4}{\\left(2x{y}^{2}\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597468038\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-397\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td>\\({\\left(5m\\right)}^{2}\\left(3{m}^{3}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Raise \\(5m\\) to the second power.<\/td>\n<td>\\({5}^{2}{m}^{2}\\cdot 3{m}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(25{m}^{2}\\cdot 3{m}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td>\\(25\\cdot 3\\cdot {m}^{2}\\cdot {m}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents.<\/td>\n<td>\\(75{m}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\({\\left(3{x}^{2}y\\right)}^{4}{\\left(2x{y}^{2}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property.<\/td>\n<td>\\(\\left({3}^{4}{x}^{8}{y}^{4}\\right)\\left({2}^{3}{x}^{3}{y}^{6}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(\\left(81{x}^{8}{y}^{4}\\right)\\left(8{x}^{3}{y}^{6}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td>\\(81\\cdot 8\\cdot {x}^{8}\\cdot {x}^{3}\\cdot {y}^{4}\\cdot {y}^{6}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents.<\/td>\n<td>\\(648{x}^{11}{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 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597466276\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597467490\" data-type=\"exercise\">\n<div id=\"fs-id1169597467492\" data-type=\"problem\">\n<p id=\"fs-id1169597467494\">Simplify: a) \\({\\left(5n\\right)}^{2}\\left(3{n}^{10}\\right)\\) b) \\({\\left({c}^{4}{d}^{2}\\right)}^{5}{\\left(3c{d}^{5}\\right)}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597466686\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597466688\">a) \\(75{n}^{12}\\) b) \\(81{c}^{24}{d}^{30}\\)<\/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 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597514234\" data-type=\"problem\">\n<p id=\"fs-id1169597514236\">Simplify: a) \\({\\left({a}^{3}{b}^{2}\\right)}^{6}{\\left(4a{b}^{3}\\right)}^{4}\\) b) \\({\\left(2x\\right)}^{3}\\left(5{x}^{7}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597456029\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169597379906\">a) \\(256{a}^{22}{b}^{24}\\) b) \\(40{x}^{10}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Multiply Monomials<\/h1>\n<p id=\"fs-id1169596310635\"><em data-effect=\"italics\">A term<\/em> in algebra is a constant or the product of a constant and one or more variables. When it is of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a whole number, it is called a monomial. Some examples of monomial are \\(8,-2{x}^{2},4{y}^{3}\\), and \\(11{z}^{7}\\).<\/p>\n\n<div id=\"fs-id1169596365842\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Monomials<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nA monomial is a term of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a positive whole number.\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597688690\">Since a monomial is an algebraic expression,we can use the properties of exponents to multiply monomials.<\/p>\n\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-id1169597507715\" data-type=\"problem\">\n<p id=\"fs-id1169597507718\">Multiply: \\(\\left(3{x}^{2}\\right)\\left(-4{x}^{3}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597508276\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-55\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\left(3{x}^{2}\\right)\\left(-4{x}^{3}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange the terms.<\/td>\n<td>\\(3\\cdot \\left(-4\\right)\\cdot {x}^{2}\\cdot {x}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(-12{x}^{5}\\)<\/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-id1169597536025\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597536029\" data-type=\"exercise\">\n<div id=\"fs-id1169597690804\" data-type=\"problem\">\n<p id=\"fs-id1169597690806\">Multiply: \\(\\left(5{y}^{7}\\right)\\left(-7{y}^{4}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597506763\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169597506765\">\\(-35{y}^{11}\\)<\/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-id1169597497499\" data-type=\"problem\">\n<p id=\"fs-id1169597501734\">Multiply: \\(\\left(-6{b}^{4}\\right)\\left(-9{b}^{5}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597479316\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169597479318\">\\(54{b}^{9}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597497493\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597497497\" data-type=\"exercise\">\n<div id=\"fs-id1169597479316\" 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-id1169597498423\" data-type=\"problem\">\n<p id=\"fs-id1169597498425\">Multiply: \\(\\left(\\dfrac{5}{6}{x}^{3}y\\right)\\left(12x{y}^{2}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597479156\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-919\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\left(\\dfrac{5}{6}{x}^{3}y\\right)\\left(12x{y}^{2}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange the terms.<\/td>\n<td>\\(\\dfrac{5}{6}\\cdot 12\\cdot {x}^{3}\\cdot x \\cdot y \\cdot {y}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(10{x}^{4}{y}^{3}\\)<\/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-id1169597508799\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597508803\" data-type=\"exercise\">\n<div id=\"fs-id1169597508805\" data-type=\"problem\">\n<p id=\"fs-id1169597508807\">Multiply: \\(\\left(\\dfrac{2}{5}{a}^{4}{b}^{3}\\right)\\left(15a{b}^{3}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597505524\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169597505526\">\\(6{a}^{5}{b}^{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<div id=\"fs-id1169597540795\" data-type=\"problem\">\n<p id=\"fs-id1169597540798\">Multiply: \\(\\left(\\dfrac{2}{3}{r}^{5}s\\right)\\left(12{r}^{6}{s}^{7}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597481388\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169597481390\">\\(8{r}^{11}{s}^{8}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597577131\" class=\"media-2\" data-type=\"note\">\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>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25MultiPropExp\">Multiplication Properties of Exponents<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169597688248\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Exponential Notation<\/strong>\n<span id=\"fs-id1169597539510\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m powder means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_016_img_new.jpg\" alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m powder means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n \t<li><strong data-effect=\"bold\">Properties of Exponents<\/strong>\n<ul id=\"fs-id1169597506748\" data-bullet-style=\"open-circle\">\n \t<li>If \\(a,b\\) are real numbers and \\(m,n\\) are whole numbers, then\n\\(\\begin{array}{lrl}\\textbf{Product Property}&amp; {a}^{m}\\cdot {a}^{n}&amp; =\u00a0 {a}^{m+n} \\\\ \\textbf{Power Property}&amp; {\\left({a}^{m}\\right)}^{n}&amp; =\u00a0 {a}^{m\\cdot n} \\\\ \\textbf{Product to a Power}&amp; {\\left(ab\\right)}^{m}&amp; =\u00a0 {a}^{m}{b}^{m} \\end{array}\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169597414232\">Simplify Expressions with Exponents<\/h2>\n<p id=\"fs-id1168745177173\">In the following exercises, simplify each expression with exponents.<\/p>\n\n<div id=\"fs-id1169597483792\" data-type=\"exercise\">\n<div id=\"fs-id1169597483794\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 424px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 124px;\">\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597483797\">1.<\/p>\na) \\({3}^{5}\\)\nb) \\({9}^{1}\\)\nc) \\({\\left(\\dfrac{1}{3}\\right)}^{2}\\)\nd) \\({\\left(0.2\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597456983\">2.<\/p>\na) \\({10}^{4}\\)\nb) \\({17}^{1}\\)\nc) \\({\\left(\\dfrac{2}{9}\\right)}^{2}\\)\nd) \\({\\left(0.5\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 124px;\">\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597691414\">3.<\/p>\na) \\({2}^{6}\\)\nb) \\({14}^{1}\\)\nc) \\({\\left(\\dfrac{2}{5}\\right)}^{3}\\)\nd) \\({\\left(0.7\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597533143\">4.<\/p>\na) \\({8}^{3}\\)\nb) \\({8}^{1}\\)\nc) \\({\\left(\\dfrac{3}{4}\\right)}^{3}\\)\nd) \\({\\left(0.4\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597485099\">5.<\/p>\na) \\({\\left(-6\\right)}^{4}\\)\nb) \\(-{6}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597483407\">6.<\/p>\na) \\({\\left(-2\\right)}^{6}\\)\nb) \\(-{2}^{6}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597690103\">7.<\/p>\na) \\(-{\\left(\\dfrac{1}{4}\\right)}^{4}\\)\nb) \\({\\left(-\\dfrac{1}{4}\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597477142\">8.<\/p>\na) \\(-{\\left(\\dfrac{2}{3}\\right)}^{2}\\)\nb) \\({\\left(-\\dfrac{2}{3}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597688278\">9.<\/p>\na) \\(-{0.5}^{2}\\)\nb) \\({\\left(-0.5\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597517780\">10.<\/p>\n\n<div id=\"fs-id1169597688274\" data-type=\"exercise\">\n<div id=\"fs-id1169597688276\" data-type=\"problem\">\n\na) \\(-{0.1}^{4}\\)\nb) \\({\\left(-0.1\\right)}^{4}\\)\n\n<\/div>\n<\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Product Property for Exponents<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168745140360\">In the following exercises, simplify each expression using the Product Property for Exponents.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">11. \\({d}^{3}\\cdot {d}^{6}\\)<\/td>\n<td style=\"width: 50%;\">12. \\({x}^{4}\\cdot {x}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. \\({n}^{19}\\cdot{n}^{12}\\)<\/td>\n<td style=\"width: 50%;\">14. \\({q}^{27}\\cdot {q}^{15}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. a) \\({4}^{5}\\cdot {4}^{9}\\) b) \\({8}^{9}\\cdot 8\\)<\/td>\n<td style=\"width: 50%;\">16. a) \\({3}^{10}\\cdot {3}^{6}\\) b) \\(5\\cdot {5}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. a) \\(y\\cdot {y}^{3}\\) b) \\({z}^{25}\\cdot {z}^{8}\\)<\/td>\n<td style=\"width: 50%;\">17. a) \\(y\\cdot {y}^{3}\\) b) \\({z}^{25}\\cdot {z}^{8}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\(w\\cdot {w}^{2}\\cdot {w}^{3}\\)<\/td>\n<td style=\"width: 50%;\">20. \\(y\\cdot {y}^{3}\\cdot {y}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. \\({a}^{4}\\cdot {a}^{3}\\cdot {a}^{9}\\)<\/td>\n<td style=\"width: 50%;\">22. \\({c}^{5}\\cdot {c}^{11}\\cdot {c}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. \\({m}^{x}\\cdot {m}^{3}\\)<\/td>\n<td style=\"width: 50%;\">24. \\({n}^{y}\\cdot {n}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. \\({y}^{a}\\cdot {y}^{b}\\)<\/td>\n<td style=\"width: 50%;\">26. \\({x}^{p}\\cdot {x}^{q}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597467039\">Simplify Expressions Using the Power Property for Exponents<\/h2>\n<p id=\"fs-id1168745238936\">In the following exercises, simplify each expression using the Power Property for Exponents.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">27. a) \\({\\left({m}^{4}\\right)}^{2}\\) b) \\({\\left({10}^{3}\\right)}^{6}\\)<\/td>\n<td style=\"width: 50%;\">28. a) \\({\\left({b}^{2}\\right)}^{7}\\) b) \\({\\left({3}^{8}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. a) \\({\\left({y}^{3}\\right)}^{x}\\) b) \\({\\left({5}^{x}\\right)}^{y}\\)<\/td>\n<td style=\"width: 50%;\">30. a) \\({\\left({x}^{2}\\right)}^{y}\\) b) \\({\\left({7}^{a}\\right)}^{b}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597517908\">Simplify Expressions Using the Product to a Power Property<\/h2>\n<p id=\"fs-id1168745136409\">In the following exercises, simplify each expression using the Product to a Power Property.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">31. a) \\({\\left(6a\\right)}^{2}\\) b) \\({\\left(3xy\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%;\">32. a) \\({\\left(5x\\right)}^{2}\\) b) \\({\\left(4ab\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. a) \\({\\left(-4m\\right)}^{3}\\) b) \\({\\left(5ab\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%;\">34. a) \\({\\left(-7n\\right)}^{3}\\) b) \\({\\left(3xyz\\right)}^{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597539742\">Simplify Expressions by Applying Several Properties<\/h2>\n<p id=\"fs-id1168742128676\">In the following exercises, simplify each expression.<\/p>\n\n<div id=\"fs-id1169597539749\" data-type=\"exercise\">\n<div id=\"fs-id1169597539751\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 342px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597539753\">35.<\/p>\na) \\({\\left({y}^{2}\\right)}^{4}\\cdot {\\left({y}^{3}\\right)}^{2}\\)\nb) \\({\\left(10{a}^{2}b\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597536161\">36.<\/p>\na) \\({\\left({w}^{4}\\right)}^{3}\\cdot {\\left({w}^{5}\\right)}^{2}\\)\nb) \\({\\left(2x{y}^{4}\\right)}^{5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597456248\">37.<\/p>\na) \\({\\left(-2{r}^{3}{s}^{2}\\right)}^{4}\\)\nb) \\({\\left({m}^{5}\\right)}^{3}\\cdot {\\left({m}^{9}\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597687924\">38.<\/p>\na) \\({\\left(-10{q}^{2}{p}^{4}\\right)}^{3}\\)\nb) \\({\\left({n}^{3}\\right)}^{10}cdot {\\left({n}^{5}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597505769\">39.<\/p>\na) \\({\\left(3x\\right)}^{2}\\left(5x\\right)\\)\nb) \\({\\left(5{t}^{2}\\right)}^{3}{\\left(3t\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597576951\">40.<\/p>\na) \\({\\left(2y\\right)}^{3}\\left(6y\\right)\\)\nb) \\({\\left(10{k}^{4}\\right)}^{3}{\\left(5{k}^{6}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597460957\">41.<\/p>\na) \\({\\left(5a\\right)}^{2}{\\left(2a\\right)}^{3}\\)\nb) \\({\\left(\\dfrac{1}{2}{y}^{2}\\right)}^{3}{\\left(\\dfrac{2}{3}y\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597525563\">42.<\/p>\na) \\({\\left(4b\\right)}^{2}{\\left(3b\\right)}^{3}\\)\nb) \\({\\left(\\dfrac{1}{2}{j}^{2}\\right)}^{5}{\\left(\\dfrac{2}{5}{j}^{3}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597456397\">43.<\/p>\na) \\({\\left(\\dfrac{2}{5}{x}^{2}y\\right)}^{3}\\)\nb) \\({\\left(\\dfrac{8}{9}x{y}^{4}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597690303\">44.<\/p>\na) \\({\\left(2{r}^{2}\\right)}^{3}{\\left(4r\\right)}^{2}\\)\nb) \\({\\left(3{x}^{3}\\right)}^{3}{\\left({x}^{5}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597537063\">45.<\/p>\na) \\({\\left({m}^{2}n\\right)}^{2}{\\left(2m{n}^{5}\\right)}^{4}\\)\nb) \\({\\left(3p{q}^{4}\\right)}^{2}{\\left(6{p}^{6}q\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Multiply Monomials<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168742151444\">In the following exercises, multiply the terms.<\/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;\">46. \\(\\left(6{y}^{7}\\right)\\left(-3{y}^{4}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">47. \\(\\left(-10{x}^{5}\\right)\\left(-3{x}^{3}\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">48. \\(\\left(-8{u}^{6}\\right)\\left(-9u\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">49. \\(\\left(-6{c}^{4}\\right)\\left(-12c\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">50. \\(\\left(\\dfrac{1}{5}{f}^{8}\\right)\\left(20{f}^{3}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">51. \\(\\left(\\dfrac{1}{4}{d}^{5}\\right)\\left(36{d}^{2}\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">52. \\(\\left(4{a}^{3}b\\right)\\left(9{a}^{2}{b}^{6}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">53. \\(\\left(6{m}^{4}{n}^{3}\\right)\\left(7m{n}^{5}\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">54. \\(\\left(\\dfrac{4}{7}r{s}^{2}\\right)\\left(14r{s}^{3}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">55. \\(\\left(\\dfrac{5}{8}{x}^{3}y\\right)\\left(24{x}^{5}y\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">56. \\(\\left(\\dfrac{2}{3}{x}^{2}y\\right)\\left(\\dfrac{3}{4}x{y}^{2}\\right)\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">56. \\(\\left(\\dfrac{2}{3}{x}^{2}y\\right)\\left(\\dfrac{3}{4}x{y}^{2}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597540981\">Mixed Practice<\/h2>\n<p id=\"fs-id1168745578187\">In the following exercises, simplify each expression.<\/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;\">58. \\({\\left({x}^{2}\\right)}^{4}\\cdot {\\left({x}^{3}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">59. \\({\\left({y}^{4}\\right)}^{3}\\cdot {\\left({y}^{5}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">60. \\({\\left({a}^{2}\\right)}^{6}\\cdot{\\left({a}^{3}\\right)}^{8}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">61. \\({\\left({b}^{7}\\right)}^{5}\\cdot {\\left({b}^{2}\\right)}^{6}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">62. \\({\\left(2{m}^{6}\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">63. \\({\\left(3{y}^{2}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">64. \\({\\left(10{x}^{2}y\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">65. \\({\\left(2m{n}^{4}\\right)}^{5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">66. \\({\\left(-2{a}^{3}{b}^{2}\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">67. \\({\\left(-10{u}^{2}{v}^{4}\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">68. \\({\\left(\\dfrac{2}{3}{x}^{2}y\\right)}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">69. \\({\\left(\\dfrac{7}{9}p{q}^{4}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">70. \\({\\left(8{a}^{3}\\right)}^{2}{\\left(2a\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">71. \\({\\left(5{r}^{2}\\right)}^{3}{\\left(3r\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">72. \\({\\left(10{p}^{4}\\right)}^{3}{\\left(5{p}^{6}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">73. \\({\\left(4{x}^{3}\\right)}^{3}{\\left(2{x}^{5}\\right)}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">74. \\({\\left(\\dfrac{1}{2}{x}^{2}{y}^{3}\\right)}^{4}{\\left(4{x}^{5}{y}^{3}\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">75. \\({\\left(\\dfrac{1}{3}{m}^{3}{n}^{2}\\right)}^{4}{\\left(9{m}^{8}{n}^{3}\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">76. \\({\\left(3{m}^{2}n\\right)}^{2}{\\left(2m{n}^{5}\\right)}^{4}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">77. \\({\\left(2p{q}^{4}\\right)}^{3}{\\left(5{p}^{6}q\\right)}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597483603\">78.<strong data-effect=\"bold\"> Email<\/strong> Kate emails a flyer to ten of her friends and tells them to forward it to ten of their friends, who forward it to ten of their friends, and so on. The number of people who receive the email on the second round is \\({10}^{2}\\), on the third round is \\({10}^{3}\\), as shown in the table below. How many people will receive the email on the sixth round? Simplify the expression to show the number of people who receive the email.<\/p>\n\n<table id=\"fs-id1169597483640\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Round\u201d and the second column is named \u201cNumber of people.\u201d In the second row, the \u2018Round\u201d column contains the value 1 and the \u201cNumber of people\u201d column contains 10. In the third row, the \u201cRound\u201d column contains the value 2 and the \u201cNumber of people\u201d column contains 10 squared. In the fourth row, the \u201cRound\u201d column contains the value 3 and the \u201cNumber of people\u201d column contains the value 10 cubed. In the fifth row, both the \u201cRound\u201d and \u201cNumber of people\u201d columns are blank. In the sixth row, the \u201cRound\u201d column contains the value 6 and the \u201cNumber of people\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Round<\/th>\n<th data-align=\"center\" data-valign=\"top\">Number of people<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">10<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\({10}^{2}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\({10}^{3}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">6<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597538896\">79. <strong data-effect=\"bold\">Salary<\/strong> Jamal\u2019s boss gives him a 3% raise every year on his birthday. This means that each year, Jamal\u2019s salary is 1.03 times his last year\u2019s salary. If his original salary was \\$35,000, his salary after 1 year was \\(\\text{\\$}35,000\\left(1.03\\right)\\), after 2 years was \\(\\text{\\$}35,000{\\left(1.03\\right)}^{2}\\), after 3 years was \\(\\text{\\$}35,000{\\left(1.03\\right)}^{3}\\), as shown in the table below. What will Jamal\u2019s salary be after 10 years? Simplify the expression, to show Jamal\u2019s salary in dollars.<\/p>\n\n<table id=\"fs-id1169597538972\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Year\u201d and the second column is named \u201cSalary.\u201d In the second row, the \u2018Year\u201d column contains the value 1 and the \u201cSalary\u201d column contains 35,000 dollars times 1.03. In the third row, the \u201cYear\u201d column contains the value 2 and the \u201cSalary\u201d column contains 35,000 dollars times 1.03 squared. In the fourth row, the \u201cYear\u201d column contains the value 3 and the \u201cSalary\u201d column contains the value 35,000 dollars times 1.03 cubed. In the fifth row, both the \u201cYear\u201d and \u201cSalary\u201d columns are blank. In the sixth row, the \u201cYear\u201d column contains the value 10 and the \u201cSalary\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Year<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Salary<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}35,000\\left(1.03\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}35,000{\\left(1.03\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}35,000{\\left(1.03\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">10<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597686382\">80.<strong data-effect=\"bold\"> Clearance<\/strong> A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week\u2019s cost. If the original cost of a sofa was \\$1,000, the cost for the first week would be \\(\\text{\\$}1,000\\left(0.70\\right)\\) and the cost of the item during the second week would be \\(\\text{\\$}1,000{\\left(0.70\\right)}^{2}\\). Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.<\/p>\n\n<table id=\"fs-id1169597686438\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Week\u201d and the second column is named \u201cCost.\u201d In the second row, the \u2018Week\u201d column contains the value 1 and the \u201cCost\u201d column contains 1,000 dollars times .70. In the third row, the \u201cWeek\u201d column contains the value 2 and the \u201cCost\u201d column contains 1,000 dollars times .70 squared. In the fourth row, the \u201cWeek\u201d column contains the value 3 and the \u201cCost\u201d column is blank. In the fifth row both the \u201cWeek\u201d and \u201cCost\u201d columns are left blank. In the sixth row, the \u201cWeek\u201d column contains the value 8 and the \u201cCost\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Week<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Cost<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}1,000\\left(0.70\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}1,000{\\left(0.70\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">5<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597684190\">81.<strong data-effect=\"bold\"> Depreciation<\/strong> Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year\u2019s value. If a new car was purchased for ?20,000, the value at the end of the first year would be \\(\\text{\\$}20,000\\left(0.90\\right)\\) and the value of the car after the end of the second year would be \\(\\text{\\$}20,000{\\left(0.90\\right)}^{2}\\). Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.<\/p>\n\n<table id=\"fs-id1169597684245\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Week\u201d and the second column is named \u201cCost.\u201d In the second row, the \u2018Week\u201d column contains the value 1 and the \u201cCost\u201d column contains 20,000 dollars times .90. In the third row, the \u201cWeek\u201d column contains the value 2 and the \u201cCost\u201d column contains 20,000 dollars times .90 squared. In the fourth and fifth rows, the \u201cWeek\u201d column contains the values 3 and 4 while the \u201cCost\u201d column is blank. In the sixth row, the \u201cWeek\u201d column contains the value 5 and the \u201cCost\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Week<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Cost<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}20,000\\left(0.90\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(\\text{\\$}20,000{\\left(0.90\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">4<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">8<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">82. Use the Product Property for Exponents to explain why \\(x\\cdot x={x}^{2}\\).<\/td>\n<td style=\"width: 50%;\">83. Explain why \\(-{5}^{3}={\\left(-5\\right)}^{3}\\) but \\(-{5}^{4}\\ne {\\left(-5\\right)}^{4}\\).<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">84. Jorge thinks \\({\\left(\\dfrac{1}{2}\\right)}^{2}\\) is 1. What is wrong with his reasoning?<\/td>\n<td style=\"width: 50%;\">85. Explain why \\({x}^{3}\\cdot {x}^{5}\\) is \\({x}^{8}\\), and not \\({x}^{15}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">2.\u00a0a) 10,000 b) 17 c) \\(\\dfrac{4}{81}\\) d) 0.125<\/td>\n<td style=\"width: 50%;\">4. a) 512 b) 8 c) \\(\\dfrac{27}{64}\\)\u00a0d) 0.064<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">6. a) 64 b) \\(-64\\)<\/td>\n<td style=\"width: 50%;\">8. a) \\(-\\dfrac{4}{9}\\) b) \\(\\dfrac{4}{9}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">10. a) \\(-0.0001\\) b) \\(0.0001\\)<\/td>\n<td style=\"width: 50%;\">12. \\({x}^{6}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">14. \\({q}^{42}\\)<\/td>\n<td style=\"width: 50%;\">16. a) \\({3}^{16}\\) b) \\({5}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">18. a) \\({w}^{6}\\) b) \\({u}^{94}\\)<\/td>\n<td style=\"width: 50%;\">20. \\({y}^{9}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">22. \\({c}^{18}\\)<\/td>\n<td style=\"width: 50%;\">24. \\({n}^{y+2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">26. \\({x}^{p+q}\\)<\/td>\n<td style=\"width: 50%;\">28. a) \\({b}^{14}\\) b) \\({3}^{16}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">30. a) \\({x}^{2y}\\) b) \\({7}^{ab}\\)<\/td>\n<td style=\"width: 50%;\">32. a) \\(25{x}^{2}\\) b) \\(16{a}^{2}{b}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">34. a) \\(-343{n}^{3}\\) b) \\(81{x}^{4}{y}^{4}{z}^{4}\\)<\/td>\n<td style=\"width: 50%;\">36. a) \\({w}^{22}\\) b) \\(32{x}^{5}{y}^{20}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">38. a) \\(-1000{q}^{6}{p}^{12}\\) b) \\({n}^{40}\\)<\/td>\n<td style=\"width: 50%;\">40. a) \\(48{y}^{4}\\) b) \\(25,000{k}^{24}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">42. a) \\(432{b}^{5}\\) b) \\(\\dfrac{1}{200}{j}^{16}\\)<\/td>\n<td style=\"width: 50%;\">44. a) \\(128{r}^{8}\\) b) \\(\\dfrac{1}{200}{j}^{16}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">46. \\(-18{y}^{11}\\)<\/td>\n<td style=\"width: 50%;\">48. \\(72{u}^{7}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">50. \\(4{f}^{11}\\)<\/td>\n<td style=\"width: 50%;\">52. \\(36{a}^{5}{b}^{7}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">54. \\(8{r}^{2}{s}^{5}\\)<\/td>\n<td style=\"width: 50%;\">56. \\(\\dfrac{1}{2}{x}^{3}{y}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">58. \\({x}^{14}\\)<\/td>\n<td style=\"width: 50%;\">60. \\({a}^{36}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">62. \\(8{m}^{18}\\)<\/td>\n<td style=\"width: 50%;\">64. \\(1000{x}^{6}{y}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">66. \\(16{a}^{12}{b}^{8}\\)<\/td>\n<td style=\"width: 50%;\">68. \\(\\dfrac{8}{27}{x}^{6}{y}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">70. \\(1024{a}^{10}\\)<\/td>\n<td style=\"width: 50%;\">72. \\(25000{p}^{24}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">74. \\({x}^{18}{y}^{18}\\)<\/td>\n<td style=\"width: 50%;\">76. \\(144{m}^{8}{n}^{22}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">78. \\(1,000,000\\)<\/td>\n<td style=\"width: 50%;\">80. \\$168.07<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">82.\u00a0Answers will vary.<\/td>\n<td style=\"width: 50%;\">84.\u00a0Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse Multiplication Properties of Exponents\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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.","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 with exponents<\/li>\n<li>Simplify expressions using the Product Property for Exponents<\/li>\n<li>Simplify expressions using the Power Property for Exponents<\/li>\n<li>Simplify expressions using the Product to a Power Property<\/li>\n<li>Simplify expressions by applying several properties<\/li>\n<li>Multiply monomials<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Simplify Expressions with Exponents<\/h1>\n<p id=\"fs-id1169597499873\">Remember that an exponent indicates repeated multiplication of the same quantity. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d7212f543633ec455015dbbd5f558a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> means to multiply 2 by itself 4 times, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d7212f543633ec455015dbbd5f558a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> means 2 \u00b7 2 \u00b7 2 \u00b7 2<\/p>\n<p id=\"fs-id1169597431995\">Let\u2019s review the vocabulary for expressions with exponents.<\/p>\n<div id=\"fs-id1169597500173\" 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\">Exponential Notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><span id=\"fs-id1169597508648\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m power means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_06_02_001_img_new.jpg\" alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m power means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597488943\">This is read <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;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-54b488d725322353e3336ad5152f5c41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/> power.<\/p>\n<p id=\"fs-id1169597464781\">In the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2a487b91c28857bf9b3c6373f3ffdc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>, the <em data-effect=\"italics\">exponent<\/em> <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;\" \/> tells us how many times we use the <em data-effect=\"italics\">base<\/em> <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;\" \/> as a factor.<\/p>\n<p><span id=\"fs-id1169597420838\" data-type=\"media\" data-alt=\"This figure has two columns. The left column contains 4 cubed. Below this is 4 times 4 times 4, with \u201c3 factors\u201d written below in blue. The right column contains negative 9 to the fifth power. Below this is negative 9 times negative 9 times negative 9 times negative 9 times negative 9, with \u201c5 factors\u201d written below in blue.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_002_img_new.jpg\" alt=\"This figure has two columns. The left column contains 4 cubed. Below this is 4 times 4 times 4, with \u201c3 factors\u201d written below in blue. The right column contains negative 9 to the fifth power. Below this is negative 9 times negative 9 times negative 9 times negative 9 times negative 9, with \u201c5 factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1169597357034\">Before we begin working with variable expressions containing exponents, let\u2019s simplify a few expressions involving only numbers.<\/p>\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-id1169597464503\" data-type=\"problem\">\n<p id=\"fs-id1169597517035\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1086d4795a750165fde147f5dc6a58a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d867249c2289fbae7f7de6b92e25592f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30b85441f8d7a35deea4ac28f66ffa94_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;&#54;&#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;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a0f7d01277ace97264271ceaff030098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#54;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597379020\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-50\" 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-1086d4795a750165fde147f5dc6a58a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply three factors of 4.<\/td>\n<td>4 \u00b7 4 \u00b7 4<\/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-de25eb06760758d2c59eb63fca270413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" 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-d867249c2289fbae7f7de6b92e25592f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply one factor of 7.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30b85441f8d7a35deea4ac28f66ffa94_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;&#54;&#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;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca2ce2784b63c4f4d67c7b7bcfe0dd41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"75\" style=\"vertical-align: -17px;\" \/><\/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-11ea35fe7b11e8a526bfa192e43c0a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#51;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a0f7d01277ace97264271ceaff030098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#54;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8bc59aa74a4afcf3ce679d1472815243_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#54;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#54;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/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-5b65f4d4b0b45410fb9a38d7c6c6e217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#57;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" 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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597491698\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597497979\" data-type=\"exercise\">\n<div id=\"fs-id1169597446527\" data-type=\"problem\">\n<p id=\"fs-id1169597395263\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a1f24f4d8f12df52e638ec17c163d377_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#125;&#94;&#123;&#51;&#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-58ba473c33d8ad1f5d7ffddb9f36d5a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#53;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"23\" style=\"vertical-align: -1px;\" \/> c) <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;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27e9fd95928fb703aa7f9d3c35287ef0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#52;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597342610\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597367714\">a) 216 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c191882d9864395d30b0b35b37b5b467_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/> d) 0.1849<\/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-id1169597420581\" data-type=\"problem\">\n<p id=\"fs-id1169597467163\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-10fd11ea086036932c682ed905960733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#53;&#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-f0f7cf7379f1d53d1f5735beb3623b45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#49;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b14a45f202c56be1fc754d481df4c92c_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;&#125;&#123;&#53;&#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;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-925a182f2ab4f2127be1e5d50cddaa09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#50;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597532637\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597420188\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>b) 21 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2566d30fe2f727656e97e9ecddf58cc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c8bc1f982b0db73f7495cc1280fa0be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#52;&#55;&#53;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"68\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597406059\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597531640\" data-type=\"exercise\">\n<div id=\"fs-id1169597532637\" 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-id1169597411906\" data-type=\"problem\">\n<p id=\"fs-id1169597497879\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d13c46f0e2d7dba14b464d79f416f2c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23d6699811fedcb1dda7e3917a3072ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597493725\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-539\" 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-d13c46f0e2d7dba14b464d79f416f2c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply four factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31828a623ed29eb0de8f5be46c99e263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/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-401bd31f396b71bb39e304b3f50555d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/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-23d6699811fedcb1dda7e3917a3072ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply four factors of 5.<\/td>\n<td>-(5\u00a0 \u00b7 5 \u00b7 5 \u00b7 5)<\/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-2ddf1492d7b7256b0c279b657079fbcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597444745\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\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-id1169597444745\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\n<p id=\"fs-id1169597415505\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f030f29170d3e23cfadee1ce2e2d79f_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;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cded4683af1d70dec44b7ed335d9b045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597495810\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597537923\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2fddb0fc050fd5cd8cec81b9bb162aa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e9ef1c6bd7a9b6e2b87026a76cda03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" 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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597340444\" data-type=\"problem\">\n<p id=\"fs-id1169597447205\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c182062d5a3851ab076b78f02115cc97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"51\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2acbb75bbcf3744b2b2a882cd401abda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#49;&#51;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597351946\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597406596\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d212462b3a40626de440ded04d87fda3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f25789704087627e8b43b50632a73953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597448020\">Notice the similarities and differences in <a class=\"autogenerated-content\" href=\"#fs-id1169597411906\">(Example 2)<\/a> a) and <a class=\"autogenerated-content\" href=\"#fs-id1169597411906\">(Example 2)<\/a> b)! Why are the answers different? As we follow the order of operations in part a) the parentheses tell us to raise the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-59c99c20648372833a55f28a2f19deaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> to the 4<sup>th<\/sup> power. In part b) we raise just the 5 to the 4<sup>th<\/sup> power and then take the opposite.<\/p>\n<h1 data-type=\"title\">Simplify Expressions Using the Product Property for Exponents<\/h1>\n<p id=\"fs-id1169597350867\">You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too.<\/p>\n<p id=\"fs-id1169597501890\">We\u2019ll derive the properties of exponents by looking for patterns in several examples.<\/p>\n<p id=\"fs-id1169597408681\">First, we will look at an example that leads to the Product Property.<\/p>\n<table id=\"eip-id1172187661170\" class=\"grid\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the text in the left column says \u201cWhat does this mean?\u201d In the right column is x squared times x cubed. One row down, the text in the left column says \u201cHow many factors altogether?\u201d In the right column is x times x, times x times x times x. \u201c2 factors\u201d is written below x times x and \u201c3 factors\u201d is written below x times x times x. Below this is a bracket, beneath which \u201c5 factors\u201d is written in blue. One row down, the text in the left column says \u201cSo we have\u201d. In the right column is x to the fifth power. One row down, the text in the left column says \u201cNotice that 5 is the sum of the exponents, 2 and 3.\u201d In the right column is the text \u201cx squared times x cubed is x to the 2 plus 3 power, or x to the fifth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187661190\" data-type=\"media\" data-alt=\"x squared times x cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003a_img_new.jpg\" alt=\"x squared times x cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">What does this mean?<br \/>\nHow many factors altogether?<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1172187661215\" data-type=\"media\" data-alt=\"x times x, multiplied by x times x. x times x has two factors. x times x times x has three factors. 2 plus 3 is five factors.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003b_img_new.jpg\" alt=\"x times x, multiplied by x times x. x times x has two factors. x times x times x has three factors. 2 plus 3 is five factors.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>So, we have<\/td>\n<td data-align=\"left\"><span id=\"eip-id1172187661234\" data-type=\"media\" data-alt=\"x to the fifth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003c_img_new.jpg\" alt=\"x to the fifth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice that 5 is the sum of the exponents, 2 and 3.<\/td>\n<td><span id=\"eip-id1172187661250\" data-type=\"media\" data-alt=\"x squared times x cubed is x to the power of 2 plus 3, or x to the fifth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_003d_img_new.jpg\" alt=\"x squared times x cubed is x to the power of 2 plus 3, or x to the fifth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597334107\">We write:<\/p>\n<div id=\"fs-id1169597498272\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7aac2c154dee37730e1455b8540769a7_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;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#43;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"48\" style=\"vertical-align: -22px;\" \/><\/div>\n<p id=\"fs-id1169597430306\">The base stayed the same and we added the exponents. This leads to the <strong data-effect=\"bold\">Product Property for Exponents<\/strong>.<\/p>\n<div id=\"fs-id1169597397855\" 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\">Product Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597491806\">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, 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 counting numbers, then<\/p>\n<div id=\"fs-id1169597359735\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><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;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597397229\">To multiply with like bases, add the exponents.<\/p>\n<\/div>\n<p id=\"fs-id1169597410476\">An example with numbers helps to verify this property.<\/p>\n<div id=\"fs-id1169597490292\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf1e0d2fc71eacb5dbdb8d4295677ac1_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;&#99;&#108;&#125;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#43;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#51;&#50;&#38;&#32;&#61;&#32;&#38;&#32;&#51;&#50;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"126\" style=\"vertical-align: -28px;\" \/><\/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 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597484664\" data-type=\"problem\">\n<p id=\"fs-id1169597441330\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2541460e102ae33b642ed32c6ba71cba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597479966\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172188903486\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains y to the fifth power times y to the sixth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is y to the 5 plus 6 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is y to the eleventh power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172188903506\" data-type=\"media\" data-alt=\"y to the fifth power times y to the sixth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004a_img_new.jpg\" alt=\"y to the fifth power times y to the sixth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \\cdot <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172188903523\" data-type=\"media\" data-alt=\"y to the power of 5 plus 6.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004b_img_new.jpg\" alt=\"y to the power of 5 plus 6.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172188903539\" data-type=\"media\" data-alt=\"y to the eleventh power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_004c_img_new.jpg\" alt=\"y to the eleventh power.\" 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 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576688\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597478796\" data-type=\"exercise\">\n<div id=\"fs-id1169597419943\" data-type=\"problem\">\n<p id=\"fs-id1169597538332\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4ce7841cef5b3404e2a26b5d68d2574_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#98;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597536170\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597490790\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b570fc26536b1a68d7644286d2f14d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#49;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" 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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597502452\" data-type=\"problem\">\n<p id=\"fs-id1169597410315\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77a9f94a055a015c48df51fd2f1dc935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597376680\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597528228\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94d91c510fc8d9abb2188a2fcf79fcfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597495832\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597504597\" data-type=\"exercise\">\n<div id=\"fs-id1169597376680\" data-type=\"solution\">\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-id1169597397528\" data-type=\"problem\">\n<p id=\"fs-id1169597497488\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4f6ce517eef808c98760e71a7b9cf0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#50;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"45\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-624a0a4cd5a06197733664a3b7e264c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597459920\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745220462\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1172187839283\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 2 to the fifth power times 2 to the ninth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is 2 to the 5 plus 9 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 2 to the fourteenth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187839303\" data-type=\"media\" data-alt=\"2 to the fifth power times 2 to the ninth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005a_img_new.jpg\" alt=\"2 to the fifth power times 2 to the ninth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187839328\" data-type=\"media\" data-alt=\"2 to the power of 5 plus 9.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005b_img_new.jpg\" alt=\"2 to the power of 5 plus 9.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187990102\" data-type=\"media\" data-alt=\"2 to the 14th power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_005c_img_new.jpg\" alt=\"2 to the 14th power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table id=\"eip-id1172187678535\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 3 times 3 to the fourth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is 3 to the 1 plus 4 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 3 to the fifth power\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187678555\" data-type=\"media\" data-alt=\"3 to the fifth power times 3 to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006a_img_new.jpg\" alt=\"3 to the fifth power times 3 to the fourth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187678580\" data-type=\"media\" data-alt=\"3 to the power of 5 plus 4.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006b_img_new.jpg\" alt=\"3 to the power of 5 plus 4.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187678597\" data-type=\"media\" data-alt=\"3 to the ninth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_006c_img_new.jpg\" alt=\"3 to the ninth 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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597392408\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597432293\" data-type=\"exercise\">\n<div id=\"fs-id1169597523718\" data-type=\"problem\">\n<p id=\"fs-id1169597527464\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d86bd89a5d8714c9c2fdbdf74780248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#53;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abc61416774a86f15868024f4afb61e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#52;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"45\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597339458\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597389559\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a3eac14af03567c906c38e5854b7355_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#54;&#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-756cc847f1cdb2f174411c736481c4c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"23\" 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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539933\" data-type=\"problem\">\n<p id=\"fs-id1169597400959\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87b4c46003f9d03fb3e8efa7cbee95fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#55;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"45\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c3b7f963e84c45787b9b8267d99a6b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597485232\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597397173\">a) <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;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d0fd5ddc40425f9ed08155f006979da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597445862\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597526418\" data-type=\"exercise\">\n<div id=\"fs-id1169597485232\" data-type=\"solution\">\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-id1169597506773\" data-type=\"problem\">\n<p id=\"fs-id1169597447809\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a61865de65a12b934fa03b981669bae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1328be68e9bf91641b0ca3f839d3fcb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"62\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597481014\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745203075\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1172182437179\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains a to the seventh power times a. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is a to the 7 plus 1 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is a to the eighth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182437199\" data-type=\"media\" data-alt=\"a to the seventh power times a.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007a_img_new.jpg\" alt=\"a to the seventh power times a.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite, a = a<sup>1<\/sup>.<\/td>\n<td><span id=\"eip-id1172182372263\" data-type=\"media\" data-alt=\"a to the seventh power times a to the first power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007b_img_new.jpg\" alt=\"a to the seventh power times a to the first power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the product property, <em data-effect=\"italics\">a<sup>m<\/sup><\/em> \u00b7 <em data-effect=\"italics\">a<sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m+n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172182372288\" data-type=\"media\" data-alt=\"a to the power of 7 plus 1.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007c_img_new.jpg\" alt=\"a to the power of 7 plus 1.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182372304\" data-type=\"media\" data-alt=\"a to the eighth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_007d_img_new.jpg\" alt=\"a to the eighth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table id=\"eip-id1172187957456\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains x to the twenty seventh power times x to the thirteenth power. One row down, the left column says \u201cUse the product property, a to the m power times a to the n power equals a to the m plus n power.\u201d In the right column is x to the 27 plus 13 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is x to the fortieth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187957476\" data-type=\"media\" data-alt=\"x to the twenty-seventh power times x to the thirteenth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008a_img_new.jpg\" alt=\"x to the twenty-seventh power times x to the thirteenth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice, the bases are the same, so add the exponents.<\/td>\n<td><span id=\"eip-id1172187957493\" data-type=\"media\" data-alt=\"x to the power of 27 plus 13.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008b_img_new.jpg\" alt=\"x to the power of 27 plus 13.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187957510\" data-type=\"media\" data-alt=\"x to the fortieth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_008c_img_new.jpg\" alt=\"x to the fortieth 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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597502123\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597498478\" data-type=\"exercise\">\n<div id=\"fs-id1169597525992\" data-type=\"problem\">\n<p id=\"fs-id1169597517413\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8936aaa7b7cd2c0ad02ee75c49e7f5c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"39\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9bc98f7bb68f9ca88a17df27eea430f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597530042\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597535102\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-817db39aa09c98a7573e3bb9b042e8ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef9c28821f8c1b81c34f58650ec1cccb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#52;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" 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 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597690271\" data-type=\"problem\">\n<p id=\"fs-id1169597690273\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d55a165d51ce52f6dba2b39be88b4873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#122;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-857aecbaa1be1c78a46899254d3c01b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#49;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#98;&#125;&#94;&#123;&#51;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597396891\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597460764\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0d9f473e7598340f023422b99c3672b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#56;&#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-6858a6d9d0f0d2f3f4c13c66ad58fef0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597689405\">We can extend the Product Property for Exponents to more than two factors.<\/p>\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-id1169597479150\" data-type=\"problem\">\n<p id=\"fs-id1169597492751\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dafd24380bc2da737f31fe2a2a7ed909_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597691555\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187986203\" class=\"unnumbered unstyled\" style=\"height: 45px;\" summary=\"This figure has two columns. At the top of the figure, the right column contains d to the fourth power times d to the fifth power times d squared. One row down, the left column says \u201cAdd the exponents, since bases are the same.\u201d In the right column is d to the 4 plus 5 plus 2 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is d to the eleventh power.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\"><\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986223\" data-type=\"media\" data-alt=\"d to the fourth power times d to the fifth power times d squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009a_img_new.jpg\" alt=\"d to the fourth power times d to the fifth power times d squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\">Add the exponents, since bases are the same.<\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986240\" data-type=\"media\" data-alt=\"d to the power of 4 plus 5 plus 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009b_img_new.jpg\" alt=\"d to the power of 4 plus 5 plus 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 507.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 142.406px;\"><span id=\"eip-id1172187986258\" data-type=\"media\" data-alt=\"d to the eleventh power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_009c_img_new.jpg\" alt=\"d to the eleventh power.\" 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<div id=\"fs-id1169597466455\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597466458\" data-type=\"exercise\">\n<div id=\"fs-id1169597484498\" data-type=\"problem\">\n<p id=\"fs-id1169597484501\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a404611c083f8c4f86db669aa2b8d500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"78\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597508776\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597508778\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3c509287fa90f5bcff02276b127ff48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" 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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597500442\" data-type=\"problem\">\n<p id=\"fs-id1169597500445\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-771cef12acf581675218298dcf717fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#98;&#125;&#94;&#123;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#98;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577193\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597517090\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-439e06ed3f3ab27c909aa91dd48a5aad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#49;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Power Property for Exponents<\/h1>\n<p id=\"fs-id1169597461953\">Now let\u2019s look at an exponential expression that contains a power raised to a power. See if you can discover a general property.<\/p>\n<table id=\"eip-id1172188999640\" class=\"grid\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the right column contains x squared, in parentheses, cubed. One row down, the text in the left column says \u201cWhat does this mean?\u201d In the right column is x squared times x squared times x squared. One row down, the text in the left column says \u201cHow many factors altogether?\u201d In the right column is x times x, times x times x, times x times x. \u201c2 factors\u201d is written below each of the three instances of x times x. Below this is a bracket, beneath which \u201c6 factors\u201d is written in blue. One row down, the text in the left column says \u201cSo we have\u201d. In the right column is x to the sixth power. One row down, the text in the left column says \u201cNotice that 6 is the product of the exponents, 2 and 3.\u201d In the right column is \u201cx squared, in parentheses, cubed, is x to the 2 times 3 power, or x to the sixth power.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172188999660\" data-type=\"media\" data-alt=\"x squared, in parentheses, cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010a_img_new.jpg\" alt=\"x squared, in parentheses, cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">What does this mean?<br \/>\nHow many factors altogether?<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1172188999686\" data-type=\"media\" data-alt=\"x squared cubed is x squared times x squared times x squared, which is x times x, multiplied by x times x, multiplied by x times x. x times x has two factors. Two plus two plus two is six factors.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010b_img_new.jpg\" alt=\"x squared cubed is x squared times x squared times x squared, which is x times x, multiplied by x times x, multiplied by x times x. x times x has two factors. Two plus two plus two is six factors.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>So we have<\/td>\n<td><span id=\"eip-id1172188999702\" data-type=\"media\" data-alt=\"x to the sixth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010c_img_new.jpg\" alt=\"x to the sixth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice that 6 is the product of the exponents, 2 and 3.<\/td>\n<td><span id=\"eip-id1172188999719\" data-type=\"media\" data-alt=\"x squared cubed is x to the power of 2 times 3, or x to the sixth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_010d_img_new.jpg\" alt=\"x squared cubed is x to the power of 2 times 3, or x to the sixth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597422219\">We write:<\/p>\n<div id=\"fs-id1169597533352\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0dd989641b5858b1e46194d271259fde_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;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#32;&#92;&#92;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"39\" style=\"vertical-align: -23px;\" \/><\/div>\n<p id=\"fs-id1169597537342\">We multiplied the exponents. This leads to the Power Property for Exponents.<\/p>\n<div id=\"fs-id1169597577174\" 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\">Power Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597467027\">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, 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<p><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;\" \/><\/p>\n<\/div>\n<\/div>\n<p>To raise a power to a power, multiply the exponents.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597537099\">An example with numbers helps to verify this property.<\/p>\n<div id=\"fs-id1169597464874\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2cebb2bd2bbb0bd0079b68fd421fc3f4_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;&#99;&#108;&#125;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#43;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#53;&#125;&#32;&#92;&#92;&#32;&#51;&#50;&#38;&#32;&#61;&#32;&#38;&#32;&#51;&#50;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"126\" style=\"vertical-align: -28px;\" \/><\/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 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597518560\" data-type=\"problem\">\n<p id=\"fs-id1169597690624\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c921019a56c568d69c1dd6e82a95b749_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;&#57;&#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-e4676e3827f77c384bd35d8f28e2704f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#52;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597480454\" 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-id1166425254840\">a)<\/p>\n<table id=\"eip-id1172186692197\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains y to the fifth power, in parentheses, to the ninth power. One row down, the left column says \u201cUse the power property, a to the m power, in parentheses, to the n power equals a to the m times n power.\u201d In the right column is y to the 5 times 9 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is y to the forty-fifth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172186692218\" data-type=\"media\" data-alt=\"y to the fifth power, in parentheses, to the ninth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011a_img_new.jpg\" alt=\"y to the fifth power, in parentheses, to the ninth power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the power property, (<em data-effect=\"italics\">a<sup>m<\/sup><\/em>)<em data-effect=\"italics\"><sup>n<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m \u00b7 n<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172186692244\" data-type=\"media\" data-alt=\"y to the power of 5 times 9.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011b_img_new.jpg\" alt=\"y to the power of 5 times 9.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186692261\" data-type=\"media\" data-alt=\"y to the 45th power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_011c_img_new.jpg\" alt=\"y to the 45th power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<\/p>\n<table id=\"eip-id1172187801343\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 4 to the fourth power, in parentheses, to the seventh power. One row down, the left column says \u201cUse the power property, a to the m power, in parentheses, to the n power equals a to the m times n power.\u201d In the right column is 4 to the 4 times 7 power. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 4 to the twenty-eighth power.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187801363\" data-type=\"media\" data-alt=\"4 to the fourth power, in parentheses, to the 7th power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012a_img_new.jpg\" alt=\"4 to the fourth power, in parentheses, to the 7th power.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the power property.<\/td>\n<td><span id=\"eip-id1172187801380\" data-type=\"media\" data-alt=\"4 to the power of 4 times 7.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012b_img_new.jpg\" alt=\"4 to the power of 4 times 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187801396\" data-type=\"media\" data-alt=\"4 to the twenty-eighth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_012c_img_new.jpg\" alt=\"4 to the twenty-eighth power.\" 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 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597515984\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597515987\" data-type=\"exercise\">\n<div id=\"fs-id1169597691563\" data-type=\"problem\">\n<p id=\"fs-id1169597691565\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c16e26fc8f4d0cd2d50773dbe1f1bc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"37\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bec02ddfc957a3fd54edca5cf2b5e54b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#53;&#125;&#94;&#123;&#52;&#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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577234\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597505931\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75ddbbb19ee62dcb61a1e76da40f2663_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bd4a7104ac54c0bef4c122e6eb41f080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" 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-id1169597508068\" data-type=\"problem\">\n<p id=\"fs-id1169597530485\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a689cd7ef4064a7b935c537b600c003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#122;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#57;&#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-ea363c1cc27b91db2cc0fcf164aba501_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#51;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"38\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597521282\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597538336\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2d486730f102d5aa6eb02f51af1687f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#53;&#52;&#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-0afd25ce243a791b91cb83262f620629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Product to a Power Property<\/h1>\n<p id=\"fs-id1169597579504\">We will now look at an expression containing a product that is raised to a power. Can you find this pattern?<\/p>\n<table id=\"eip-416\" class=\"grid\" 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-3fbb673da6f79e00868924ea34b41c73_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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>What does this mean?<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d400f45f80883d1ff4abb5eee5a4239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"83\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>We group the like factors together.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27412daaeaea67736011692b256fdbd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"121\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>How many factors of 2 and 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;\" \/>?<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-531a8c023df147e7d4c54eeb1a758c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597540864\">Notice that each factor was raised to the power and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fbb673da6f79e00868924ea34b41c73_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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-531a8c023df147e7d4c54eeb1a758c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<table id=\"eip-300\" style=\"width: 100%;\" 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-3fbb673da6f79e00868924ea34b41c73_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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/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-531a8c023df147e7d4c54eeb1a758c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597577372\">The exponent applies to each of the factors! This leads to the Product to a Power Property for Exponents.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Product to a Power Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597542287\">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;\" \/> is a whole number, then<\/p>\n<p><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;\" \/><\/p>\n<p>To raise a product to a power, raise each factor to that power.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597688061\">An example with numbers helps to verify this property:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa746674021965d61be063c2f42884da_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;&#99;&#108;&#125;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#32;&#123;&#54;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#32;&#38;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#32;&#92;&#92;&#32;&#32;&#51;&#54;&#38;&#32;&#61;&#32;&#38;&#32;&#51;&#54;&#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=\"69\" width=\"143\" style=\"vertical-align: -28px;\" \/><\/p>\n<div data-type=\"equation\" data-label=\"\">\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-id1169597541988\" data-type=\"problem\">\n<p id=\"fs-id1169597541990\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4bbe0826dc6299a4c9f24374ab89c622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#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-7c405d667ac9c810e566c657d18f5221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#109;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597448611\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1168745206751\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1172182438507\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains negative 9d squared. One row down, the left column says \u201cUse Power of a Product Property, ab to the m power equals a to the m power b to the m power.\u201d In the right column is negative 9 squared d squared. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 81d squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182437006\" data-type=\"media\" data-alt=\"Negative 9 d squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013a_img_new.jpg\" alt=\"Negative 9 d squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use Power of a Product Property, (<em data-effect=\"italics\">ab<\/em>)<em data-effect=\"italics\"><sup>m<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m<\/sup>b<sup>m<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172182437032\" data-type=\"media\" data-alt=\"negative 9 squared d squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013b_img_new.jpg\" alt=\"negative 9 squared d squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172182437048\" data-type=\"media\" data-alt=\"81 d squared.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_013c_img_new.jpg\" alt=\"81 d squared.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table id=\"eip-id1172187986280\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains 3mn cubed. One row down, the left column says \u201cUse Power of a Product Property, ab to the m power equals a to the m power b to the m power.\u201d In the right column is 3 cubed m cubed n cubed. One row down, the text on the left says \u201cSimplify.\u201d In the right column is 27m cubed n cubed.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187986300\" data-type=\"media\" data-alt=\"3 m n cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014a_img_new.jpg\" alt=\"3 m n cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use Power of a Product Property, (<em data-effect=\"italics\">ab<\/em>)<em data-effect=\"italics\"><sup>m<\/sup><\/em> = <em data-effect=\"italics\">a<sup>m<\/sup>b<sup>m<\/sup><\/em>.<\/td>\n<td><span id=\"eip-id1172187986327\" data-type=\"media\" data-alt=\"3 cubed m cubed n cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014b_img_new.jpg\" alt=\"3 cubed m cubed n cubed.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187986344\" data-type=\"media\" data-alt=\"27 m cubed n cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_014c_img_new.jpg\" alt=\"27 m cubed n cubed.\" 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 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597508854\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597508858\" data-type=\"exercise\">\n<div id=\"fs-id1169597538092\" data-type=\"problem\">\n<p id=\"fs-id1169597538094\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78b4e97417ec8cd916d1a744593a2c72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"61\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c9acf14c857c766af4382cffb3e28a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#119;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597512464\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597512466\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35675e4bf683d0ce1de099a3d61cda71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b8cf78a440a665ea447646e9934458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#123;&#119;&#125;&#94;&#123;&#53;&#125;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597460895\" data-type=\"problem\">\n<p id=\"fs-id1169597460897\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6dfc27669b6fa5c6e7a98ead72db4f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#119;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#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-57d34daa29e40b026f8f784f7a4f71d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597518878\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597518880\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d022dd2c07e36d9e1aab10f22d2693ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#53;&#123;&#119;&#125;&#94;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e70e6c1b343e79be3e1934d21690a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Applying Several Properties<\/h1>\n<p id=\"fs-id1169597516917\">We now have three properties for multiplying expressions with exponents. Let\u2019s summarize them and then we\u2019ll do some examples that use more than one of the properties.<\/p>\n<div id=\"fs-id1169597538041\" 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\">Properties of Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597503103\">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-536\" 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-02ffcc1c44ee891ae66f868ad083d296_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;&#32;&#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-7af37fe1ceaf45a4736d45f1fe379be5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#41;&#94;&#123;&#110;&#125;&#32;&#61;&#32;&#32;&#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-dec11b5b7c04104f554aaff11e86125a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#97;&#98;&#41;&#94;&#123;&#109;&#125;&#32;&#61;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>All exponent properties hold true for any real numbers<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;\" \/>. Right now, we only use whole number exponents.<\/p>\n<\/div>\n<\/div>\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 id=\"fs-id1169597466702\" data-type=\"problem\">\n<p id=\"fs-id1169597466704\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ddf7ee3db2efd2684003c7bf6290dc08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#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;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dab4e1173b6393c7f3bb870719dd810c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#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=\"79\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597689335\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-886\" style=\"width: 100%;\" 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-ddf7ee3db2efd2684003c7bf6290dc08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#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;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad095c785e1e39687a2639861afd0af9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d7707913d5118752e07129fb03b3fc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/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-dab4e1173b6393c7f3bb870719dd810c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#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=\"79\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2904d54e950eaf3f3bae577b6395f39a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#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=\"125\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c04797b102c6989d06f3429fb1d83e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/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-6199020ecf9d24c5f5d45b8935c2716e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"59\" 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-id1169597516190\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597485072\" data-type=\"exercise\">\n<div id=\"fs-id1169597485074\" data-type=\"problem\">\n<p id=\"fs-id1169597485076\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51fcf25194ad953e54a08cd559225048_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f23af585458599cf999a0b054326cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#99;&#125;&#94;&#123;&#52;&#125;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"76\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597467471\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597467473\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b47f877c876b2e9471d8f729658241e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#52;&#56;&#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-31d130ddbe2ee8e7855ba862c58c80a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#99;&#125;&#94;&#123;&#49;&#50;&#125;&#123;&#100;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" 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-id1169597467696\" data-type=\"problem\">\n<p id=\"fs-id1169597467597\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9da00c0045e7d54826cddc8e277bb9ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ed51dbf6c4505846ce1c2c8258b8b18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"78\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597467809\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597467812\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ddb1804e16a52b766eb09bfb27f23620_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#120;&#125;&#94;&#123;&#50;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b97189bb717d20eb56d18cf642055e40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597467690\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597467694\" data-type=\"exercise\">\n<div id=\"fs-id1169597467809\" data-type=\"solution\">\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-id1169597467921\" data-type=\"problem\">\n<p id=\"fs-id1169597467923\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c6263b6cc7ffc56616475b6ad75ae89e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"94\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d2204e7847c827f7fd535c4d73b7a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"117\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597468038\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-397\" 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-c6263b6cc7ffc56616475b6ad75ae89e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"94\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Raise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20bab037c30316b21529ae93542741a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"24\" style=\"vertical-align: 0px;\" \/> to the second power.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f40a440639cac68dff2dba0c2479c7f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#50;&#125;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" 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-f16a069f2f041295d9c0e26d9bae1606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb4682e70669813b8b8613109e2c9604_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"111\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-392672b199c8f2c20d4e9ea3b2cba97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#53;&#123;&#109;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/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-5d2204e7847c827f7fd535c4d73b7a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"117\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Product to a Power Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c078309238b2dd26c630e47115b3e849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#51;&#125;&#94;&#123;&#52;&#125;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\" \/><\/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-5db75d393af7be162ab8a3fc48a532b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#49;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b15892122ca7e574d41eb6d4a42e450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c45ad1c6c17e5c9c73d52f24373c05d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#56;&#123;&#120;&#125;&#94;&#123;&#49;&#49;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" 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 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597466276\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597467490\" data-type=\"exercise\">\n<div id=\"fs-id1169597467492\" data-type=\"problem\">\n<p id=\"fs-id1169597467494\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8228ee0fa68985ef718897e15611dd53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#110;&#125;&#94;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"91\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d6a192b42aefb0455bd7520e6476c46d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#52;&#125;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#99;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"111\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597466686\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597466688\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fe7b57f4bcae44788772c1ea3ece042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#53;&#123;&#110;&#125;&#94;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a17c23bf58ae02111d3dabe3a1a3630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#99;&#125;&#94;&#123;&#50;&#52;&#125;&#123;&#100;&#125;&#94;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -1px;\" \/><\/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 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597514234\" data-type=\"problem\">\n<p id=\"fs-id1169597514236\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0249bc7149d12fca5b474dc1a7044fce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#97;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"111\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6db2edbf233f25eca7086e1461d83bd_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;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"83\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597456029\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597379906\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0742165683e678e73bd360c392138ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33616e101195a0fd076be8fdbd963992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Multiply Monomials<\/h1>\n<p id=\"fs-id1169596310635\"><em data-effect=\"italics\">A term<\/em> in algebra is a constant or the product of a constant and one or more variables. When it is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46b032d64f672bab7376a968602a1f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <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 constant 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 whole number, it is called a monomial. Some examples of monomial are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb5233e61fcf84039fb0a9a07b92b3cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#44;&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81ba1829237c7bc91775ad9283d063ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#122;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1169596365842\" 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\">Monomials<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A monomial is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46b032d64f672bab7376a968602a1f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <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 constant 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 positive whole number.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597688690\">Since a monomial is an algebraic expression,we can use the properties of exponents to multiply monomials.<\/p>\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-id1169597507715\" data-type=\"problem\">\n<p id=\"fs-id1169597507718\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c060cb4be436cd4e518c471f93d9b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597508276\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-55\" 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-17c060cb4be436cd4e518c471f93d9b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4350ad481149c15fc749097d078bf54b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -5px;\" \/><\/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-258f6422cbd09b3dbb92705fca4cd822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" 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 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536025\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597536029\" data-type=\"exercise\">\n<div id=\"fs-id1169597690804\" data-type=\"problem\">\n<p id=\"fs-id1169597690806\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c800c0cfed378583bcf9207a1a283db1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597506763\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597506765\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e71a34a30fbbdb19fb0a8dc2f3f61311_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#53;&#123;&#121;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" 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 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597497499\" data-type=\"problem\">\n<p id=\"fs-id1169597501734\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9be9eb3b31b24f523c88c5b11c3c56a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597479316\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597479318\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c710e8a163d832703c50c9f794a7d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;&#123;&#98;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597497493\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597497497\" data-type=\"exercise\">\n<div id=\"fs-id1169597479316\" 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-id1169597498423\" data-type=\"problem\">\n<p id=\"fs-id1169597498425\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cdbf4d79506668a06f52be48ec01ad47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"125\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597479156\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-919\" 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-cdbf4d79506668a06f52be48ec01ad47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"125\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8202f4f80d7d24f905667346802d4597_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"146\" 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-c344f731889ca0b174f2d4c5a867aa64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" 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 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597508799\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597508803\" data-type=\"exercise\">\n<div id=\"fs-id1169597508805\" data-type=\"problem\">\n<p id=\"fs-id1169597508807\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e052ab732088784fe70eaf7eebba638_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#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;&#49;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"128\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597505524\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597505526\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-358930741e27e8087988b4bf38e5722a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#123;&#98;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" 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 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597540795\" data-type=\"problem\">\n<p id=\"fs-id1169597540798\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99ab963685a985b93e9753ae6cc39865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#123;&#115;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"127\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597481388\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597481390\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bbf0f230c3b7131ac0fd392e11302821_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#114;&#125;&#94;&#123;&#49;&#49;&#125;&#123;&#115;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597577131\" class=\"media-2\" data-type=\"note\">\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>\n<li><a href=\"https:\/\/openstax.org\/l\/25MultiPropExp\">Multiplication Properties of Exponents<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169597688248\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Exponential Notation<\/strong><br \/>\n<span id=\"fs-id1169597539510\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m powder means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_06_02_016_img_new.jpg\" alt=\"This figure has two columns. In the left column is a to the m power. The m is labeled in blue as an exponent. The a is labeled in red as the base. In the right column is the text \u201ca to the m powder means multiply m factors of a.\u201d Below this is a to the m power equals a times a times a times a, followed by an ellipsis, with \u201cm factors\u201d written below in blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Properties of Exponents<\/strong>\n<ul id=\"fs-id1169597506748\" 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<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bd4bfa40ed0b011a6f9c60b70f9b5a41_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;&#108;&#114;&#108;&#125;&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#80;&#114;&#111;&#100;&#117;&#99;&#116;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#38;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#38;&#32;&#61;&#32;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#43;&#110;&#125;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#80;&#111;&#119;&#101;&#114;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#38;&#32;&#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;&#38;&#32;&#61;&#32;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#80;&#114;&#111;&#100;&#117;&#99;&#116;&#32;&#116;&#111;&#32;&#97;&#32;&#80;&#111;&#119;&#101;&#114;&#125;&#38;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#38;&#32;&#61;&#32;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"323\" style=\"vertical-align: -27px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169597414232\">Simplify Expressions with Exponents<\/h2>\n<p id=\"fs-id1168745177173\">In the following exercises, simplify each expression with exponents.<\/p>\n<div id=\"fs-id1169597483792\" data-type=\"exercise\">\n<div id=\"fs-id1169597483794\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 424px;\">\n<tbody>\n<tr style=\"height: 124px;\">\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597483797\">1.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da353cf6d44a4f332657a94e056bd385_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8692cbc1ebeb80fd52d188c9db8b0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97375d6cc3f36f238e6ccf35155b9c7c_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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"43\" style=\"vertical-align: -17px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72c53b982102a49d51d17754b67ac4d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597456983\">2.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-db678b6a192308f53bf797f17e2729bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#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-804da7bc995a50a5fc62920c242e7f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#55;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"23\" style=\"vertical-align: -1px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec61eb09e6aa652deb1abfb6e7d24a4f_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;&#125;&#123;&#57;&#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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73ac54808b7f7695a0463567f2512e42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 124px;\">\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597691414\">3.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f18c7dd00726adb39604e4b67bf29e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-981977386d3f5f9497045e7603a1ae71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#52;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"23\" style=\"vertical-align: -1px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b14a45f202c56be1fc754d481df4c92c_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;&#125;&#123;&#53;&#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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95a229256323cb9f643b118fc65d6eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 124px;\">\n<p id=\"fs-id1169597533143\">4.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d37f7552ef609926a3d2fb08b1d5e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bce21f1b54276ab1a99b41986c15ea88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d7bbf15182e7bc4b71a899449486e9d_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;&#52;&#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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3cf09141dbe9ab6039060107325d5ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597485099\">5.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8edc10fd45bf4085aa6ece9e3bb867b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4b3a5922ecd162db953911e8a6b5987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#54;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597483407\">6.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3d91d19a200676911902f50f3ee4e43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-577b07111bf2f9da6fc1d50d69d329b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#50;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597690103\">7.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a65597f7a41201ea643f672a8c3467d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"59\" style=\"vertical-align: -17px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f8257ca29944b3848b563ebeaace4f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"57\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597477142\">8.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbf0b9a0651e692e1d11f1ddf1947e8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"59\" style=\"vertical-align: -17px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7921dc34f28c6164b602e588115fb9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"57\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597688278\">9.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05cab4013dd0912f191912faef26fcf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#48;&#46;&#53;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b9b7c8302e534e644cfa48921f73f32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597517780\">10.<\/p>\n<div id=\"fs-id1169597688274\" data-type=\"exercise\">\n<div id=\"fs-id1169597688276\" data-type=\"problem\">\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3a18fb3e287abbd3ac8a28107351ede_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#48;&#46;&#49;&#125;&#94;&#123;&#52;&#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-4eda626740cdd579249001725fe187e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Product Property for Exponents<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168745140360\">In the following exercises, simplify each expression using the Product Property for Exponents.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5bfebfb72beda8b5d06a0fb2c368831_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#100;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfacfd457a6e653ea60060d9cbf9e5cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b44f469a836f1d2c6a88ab436bee910b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#49;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#110;&#125;&#94;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f967ef07ce2f69b5968ad2757ec0379_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#113;&#125;&#94;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f7011d7b07c5c0acedfd60d62ea043b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#52;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"45\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-449a318cf7790779f4807768782ad63d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">16. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7894d70b6f61f8d643743eecfe922358_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#49;&#48;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#51;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2d9f46fc8ba4e6e003838a5d9d27a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#53;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5da4fb077eac15b96c9752c0906eb6e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e685e48b9d6e8fade1dfde5d3fcfd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#122;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">17. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5da4fb077eac15b96c9752c0906eb6e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e685e48b9d6e8fade1dfde5d3fcfd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#122;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1100b49123ff2c6e12bee13d5997a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#119;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe8555693e96c4929a51ee3c57b15837_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7fc8757fbc78bbb66b9af5faff52a14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#97;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e03aced8920d6c4b53b109e3b649081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#99;&#125;&#94;&#123;&#49;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02134e8c096c56e8055ef7a854cae4b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#120;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b339b7114d070c89d5f3255fb72fa36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#121;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cbc6e2f9203f0da833f5a1902b4f7eee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c60757b17288bd5a5340c34c2bf0370f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#112;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597467039\">Simplify Expressions Using the Power Property for Exponents<\/h2>\n<p id=\"fs-id1168745238936\">In the following exercises, simplify each expression using the Power Property for Exponents.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">27. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f8022d2f3d031466017591fe41b477a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"45\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4635811969075ca66aee370b51fdbfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">28. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4656c4fe5c441fd564616c0ff9d4b360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"37\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a23cd7b8381b57b0bcd1ffc9216d85b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#51;&#125;&#94;&#123;&#56;&#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 style=\"width: 50%;\">29. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12da36d132cc74a45bee9077416231bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8370cb47566cdb98f4e877298a3f3d52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#53;&#125;&#94;&#123;&#120;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">30. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4bf87af514fadd471e365d4149bf2646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1b49bc872b1d27db8ce4941cc9bff63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#55;&#125;&#94;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597517908\">Simplify Expressions Using the Product to a Power Property<\/h2>\n<p id=\"fs-id1168745136409\">In the following exercises, simplify each expression using the Product to a Power Property.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">31. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dca9780c03fb38ed358ee9d4e0941c5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"38\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d99f12ef8b228a542fcd1ff6aa2c0e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">32. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7494e9e337a4716cf21ecfa37b22b7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e0ff773f037eb137d1d9a5da077a53f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97e56709ead08890776b47682c558858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"58\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d62db5c33044cf940c881a3e7295a7af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">34. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68a6b669202cf54725db19eafabf005d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf9707fd19496fc39c5f5800d5357c46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#121;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597539742\">Simplify Expressions by Applying Several Properties<\/h2>\n<p id=\"fs-id1168742128676\">In the following exercises, simplify each expression.<\/p>\n<div id=\"fs-id1169597539749\" data-type=\"exercise\">\n<div id=\"fs-id1169597539751\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 342px;\">\n<tbody>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597539753\">35.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84f7742cd64add9341d328e73ac5bf11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"92\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ba099fa1f61978e0aea46092ec7cf13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"64\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597536161\">36.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e5dc6d40a48d9188de644adb886e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#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=\"100\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4aecd6bd2aef882710d5749224571d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 92px;\">\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597456248\">37.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4466a28a99e036d3985175c4bd198c43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"76\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05685d71fdbc31ae3c217b4ee902eabb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 92px;\">\n<p id=\"fs-id1169597687924\">38.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3358dd381c7941bb1184c8768434155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"86\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e74f6fd8761b17d9c02538a6fa03270d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#49;&#48;&#125;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#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=\"121\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 76px;\">\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597505769\">39.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c4ed59db0a83e9742e3a0fe91b9f362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"74\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68e12e4cf7aa36fd3ef6d082979d43e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"81\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 76px;\">\n<p id=\"fs-id1169597576951\">40.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9003c867a8097dff8e5e72675aa89723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"73\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46c6eccd235db776d62e1bf11c125175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#107;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#107;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"107\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597460957\">41.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f41c02a5c41aa80bbe45c8b9db21fb11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"78\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-049ff7b99be747bfc8c187fcee1fa2fc_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;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"116\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597525563\">42.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e97c78f839922b1a23303b9fda9517a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"74\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1843b3a204d343acdf158e9b10c43a31_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;&#50;&#125;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#123;&#106;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"121\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597456397\">43.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9953a52e359b6f7f77044405755bef3e_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;&#125;&#123;&#53;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"70\" style=\"vertical-align: -17px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d9feaee070f6c17dab4cc3fefe19bb7_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;&#56;&#125;&#123;&#57;&#125;&#120;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"70\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597690303\">44.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdf8b363a310f2d8599712af49ddd91b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#114;&#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;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"85\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9575166d36c53c36f30a8fc128ec025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"90\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">\n<p id=\"fs-id1169597537063\">45.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a8dbb68f3558f77d0ed03c20fa10b46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"122\" style=\"vertical-align: -7px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf2e5fa564259b509bab7d80f1f0012f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"113\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Multiply Monomials<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168742151444\">In the following exercises, multiply the terms.<\/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;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31c3322fce516081c74616b2075ed0e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c541d34c713f8ba8d86b3ddee047fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f860f4cac507668ac835af46c59be7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#123;&#117;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#117;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"104\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba99dfdab22207ef5bef22bc1497e436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#99;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5be11adfe9936588ad1492f10b7b698a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#123;&#102;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#123;&#102;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"107\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38c64589063f844e92e0b0291383394a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#54;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"104\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e61e2169b7491a4f440977b5c451db2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"106\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a550ef75f8e8be7e6586e6e697ea17ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#109;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3cdc741323aaa94630b68310b594a60c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#55;&#125;&#114;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#114;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"120\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-195b9719a6a51b5b76245ee866c5b60f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#52;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"125\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70cef28adac3fd38b6a9bea1f395742b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"129\" style=\"vertical-align: -17px;\" \/><\/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-70cef28adac3fd38b6a9bea1f395742b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"129\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597540981\">Mixed Practice<\/h2>\n<p id=\"fs-id1168745578187\">In the following exercises, simplify each expression.<\/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;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-10c867861833bb23bf07436464ad0420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"94\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b4d758a501b7d4cd5dd2279ac4bcbd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#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=\"92\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eac8c7c1505a4c0a2fe19c871d7ab2e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"92\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4647d56b2a3207d2ae5130ddc8cd5f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"89\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c1c5a86525be5267a2bfb100be04036_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"53\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b79f096bf3ee59ba8154f36004e1ddb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-09c114e099c5debe43e0e09978879843_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"66\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-802ba20e5c3fc53f5656ab3815e2bb45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"64\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97f08689eebbb036d586e0d20e419a42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"76\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d23743dc4e12871fe9f57927ad3d0e1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"88\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e573ba52f58ef703232392eec7efe6f_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;&#125;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"70\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0068c8c11c1fb2bb43e91ffb7f539a6a_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;&#125;&#123;&#57;&#125;&#112;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"68\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca497de59cdedac45e359f1f8182200e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"87\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-42538818833187d53673e2febdea5f4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"85\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66e042f8509f77149609ddd49636e7f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee4d8a2d4fefb1224c7d0b0a1aab8f65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"99\" 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-eb3b4584e778646c7700ab26c2e2edda_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;&#50;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"145\" style=\"vertical-align: -17px;\" \/><\/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-51eaf72fb11b19599d944b09aad57dec_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;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"159\" style=\"vertical-align: -17px;\" \/><\/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-dd177f18bc699dca400ee60232435222_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"131\" 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-181ff90ca43f02326b2071956629e636_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"113\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597483603\">78.<strong data-effect=\"bold\"> Email<\/strong> Kate emails a flyer to ten of her friends and tells them to forward it to ten of their friends, who forward it to ten of their friends, and so on. The number of people who receive the email on the second round is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb380f9ccbc313090e195e368ddfdddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/>, on the third round is <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;\" \/>, as shown in the table below. How many people will receive the email on the sixth round? Simplify the expression to show the number of people who receive the email.<\/p>\n<table id=\"fs-id1169597483640\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Round\u201d and the second column is named \u201cNumber of people.\u201d In the second row, the \u2018Round\u201d column contains the value 1 and the \u201cNumber of people\u201d column contains 10. In the third row, the \u201cRound\u201d column contains the value 2 and the \u201cNumber of people\u201d column contains 10 squared. In the fourth row, the \u201cRound\u201d column contains the value 3 and the \u201cNumber of people\u201d column contains the value 10 cubed. In the fifth row, both the \u201cRound\u201d and \u201cNumber of people\u201d columns are blank. In the sixth row, the \u201cRound\u201d column contains the value 6 and the \u201cNumber of people\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Round<\/th>\n<th data-align=\"center\" data-valign=\"top\">Number of people<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">10<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb380f9ccbc313090e195e368ddfdddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><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<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">6<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597538896\">79. <strong data-effect=\"bold\">Salary<\/strong> Jamal\u2019s boss gives him a 3% raise every year on his birthday. This means that each year, Jamal\u2019s salary is 1.03 times his last year\u2019s salary. If his original salary was &#36;35,000, his salary after 1 year was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b9cf396aed2b9f6241b0653afe7a460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/>, after 2 years was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c486962b263d025b1bfd054cadaac17d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/>, after 3 years was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a55f93f646edcd6a19e6257cfffcfe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/>, as shown in the table below. What will Jamal\u2019s salary be after 10 years? Simplify the expression, to show Jamal\u2019s salary in dollars.<\/p>\n<table id=\"fs-id1169597538972\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Year\u201d and the second column is named \u201cSalary.\u201d In the second row, the \u2018Year\u201d column contains the value 1 and the \u201cSalary\u201d column contains 35,000 dollars times 1.03. In the third row, the \u201cYear\u201d column contains the value 2 and the \u201cSalary\u201d column contains 35,000 dollars times 1.03 squared. In the fourth row, the \u201cYear\u201d column contains the value 3 and the \u201cSalary\u201d column contains the value 35,000 dollars times 1.03 cubed. In the fifth row, both the \u201cYear\u201d and \u201cSalary\u201d columns are blank. In the sixth row, the \u201cYear\u201d column contains the value 10 and the \u201cSalary\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Year<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Salary<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b9cf396aed2b9f6241b0653afe7a460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c486962b263d025b1bfd054cadaac17d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a55f93f646edcd6a19e6257cfffcfe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#51;&#53;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">10<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597686382\">80.<strong data-effect=\"bold\"> Clearance<\/strong> A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week\u2019s cost. If the original cost of a sofa was &#36;1,000, the cost for the first week would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f226818e5b0ba7015390b8d65ea523d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#49;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -5px;\" \/> and the cost of the item during the second week would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a1751b32578a12c6e852df8106bdad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#49;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -5px;\" \/>. Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.<\/p>\n<table id=\"fs-id1169597686438\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Week\u201d and the second column is named \u201cCost.\u201d In the second row, the \u2018Week\u201d column contains the value 1 and the \u201cCost\u201d column contains 1,000 dollars times .70. In the third row, the \u201cWeek\u201d column contains the value 2 and the \u201cCost\u201d column contains 1,000 dollars times .70 squared. In the fourth row, the \u201cWeek\u201d column contains the value 3 and the \u201cCost\u201d column is blank. In the fifth row both the \u201cWeek\u201d and \u201cCost\u201d columns are left blank. In the sixth row, the \u201cWeek\u201d column contains the value 8 and the \u201cCost\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Week<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Cost<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f226818e5b0ba7015390b8d65ea523d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#49;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a1751b32578a12c6e852df8106bdad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#49;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">5<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169597684190\">81.<strong data-effect=\"bold\"> Depreciation<\/strong> Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year\u2019s value. If a new car was purchased for ?20,000, the value at the end of the first year would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-894c6307f57c176befa04d5b370e7503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#50;&#48;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#57;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/> and the value of the car after the end of the second year would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96817f56bd658efc7ef49bd883069383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#50;&#48;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#57;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/>. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.<\/p>\n<table id=\"fs-id1169597684245\" class=\"unnumbered\" summary=\"This table has six rows and two columns. The top row is a header row, and each of the two cells names the column beneath it. The first column is named \u2018Week\u201d and the second column is named \u201cCost.\u201d In the second row, the \u2018Week\u201d column contains the value 1 and the \u201cCost\u201d column contains 20,000 dollars times .90. In the third row, the \u201cWeek\u201d column contains the value 2 and the \u201cCost\u201d column contains 20,000 dollars times .90 squared. In the fourth and fifth rows, the \u201cWeek\u201d column contains the values 3 and 4 while the \u201cCost\u201d column is blank. In the sixth row, the \u201cWeek\u201d column contains the value 5 and the \u201cCost\u201d column contains a question mark.\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Week<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Cost<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-894c6307f57c176befa04d5b370e7503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#50;&#48;&#44;&#48;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#57;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96817f56bd658efc7ef49bd883069383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#125;&#50;&#48;&#44;&#48;&#48;&#48;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#57;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">4<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u2026<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">8<\/td>\n<td data-align=\"center\" data-valign=\"top\">?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">82. Use the Product Property for Exponents to explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-658e3124de2a6c7ad7c831efabb301e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"74\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%;\">83. Explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4defa25994b1279e4ad12ed4d87972db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -5px;\" \/> but <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b27393500a1f92aef322aded2dbe8c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#52;&#125;&#92;&#110;&#101;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">84. Jorge thinks <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-11e67f440209647fd29c7c13eb43394b_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;&#50;&#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;\" \/> is 1. What is wrong with his reasoning?<\/td>\n<td style=\"width: 50%;\">85. Explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a9f3432a3f4a6d718e1a471362e0373_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770c8867ff7afffa76d8ba308075a618_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>, and not <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46b65f026c142bb74593cc0e4c429550_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">2.\u00a0a) 10,000 b) 17 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e6bab73a2f1514f7201fdebcf2ccd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#56;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\" \/> d) 0.125<\/td>\n<td style=\"width: 50%;\">4. a) 512 b) 8 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5484d61eebce0f9cfa015b7780e522de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\" \/>\u00a0d) 0.064<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">6. a) 64 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d47325be40c0ee5b346187292f647b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">8. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d410f4ec7d4306f496436e59ff2c3ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#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-0518658dad0ca2beb20f2cce3678bdd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">10. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38276a4cc7689c366c84845b0425e7ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#48;&#46;&#48;&#48;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7136c2538cb3d86075e002415940f8ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ade694690dad929018ebadb1c3acd5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-736afcad79a8055268d750825de26260_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#52;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">16. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-163062b8bb5c27684e0e97a730e55a4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#49;&#54;&#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-16387037772fac23b0671c258f7a8ca1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">18. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad285054745da852c0554072ecf83ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a888ffb13d2ca2125ca30c36ea441c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#57;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa51bf66e107b7889321c132eb208c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#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%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1c596b1a697e501aafd8003d6d34805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49eec94e77f08e359fed4f7d896b0d1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#121;&#43;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"36\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8bac8e6c5d4da7dc2d5bfb4872a6fa2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#112;&#43;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">28. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-86b5c231b0119ba6a6670629b07f13b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-163062b8bb5c27684e0e97a730e55a4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">30. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb5db213ef47eda2e4d4f1a5e007eaa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb19e49929062127b4c46d0aa72e5a9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#97;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">32. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07288c5e6c8d99d7a9ede77241ff58ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ee08c847383668c2ec62857a97a9786_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">34. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c361d446633a1fe976452ad950ad4c28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#52;&#51;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4c20df8b521ac1b19587c926922371d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#123;&#122;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">36. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24011c21fafc52ad54bf28e5e55fa0f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-16efd77027f25d10b5868787d28c6112_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">38. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b739e75873315a3767f5a58bea5d1206_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#48;&#48;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#123;&#112;&#125;&#94;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ecbcd52418ad2c5b521f43b7d2b730a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">40. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c9e61f508b8584c4faafcaacdde0eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-289e7bb9b241cfafd1eafefab5ddeb83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#44;&#48;&#48;&#48;&#123;&#107;&#125;&#94;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">42. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ea69128553655d261d06eaac1e40793f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#51;&#50;&#123;&#98;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-250f92fadb8071c804c6f1d987b0435a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#48;&#48;&#125;&#123;&#106;&#125;&#94;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%;\">44. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2a570b6d0ee9e1b4fd29050a7be3dc89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#56;&#123;&#114;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-250f92fadb8071c804c6f1d987b0435a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#48;&#48;&#125;&#123;&#106;&#125;&#94;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"51\" style=\"vertical-align: -12px;\" \/><\/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-cc2fb792106a6e85bba5d3e5f43350ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#123;&#121;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ade0f08a58d29ed50429fc4b3f0554eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;&#123;&#117;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/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-f0ba5f9a6eecadd6b26705a41da8b7de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#102;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" 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-d2cf7ea6c5b57625208efc39753ad62d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#123;&#98;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" 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-d9cca8d378c538522698f2497815aa50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" 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-e69081037e87d7159c13b73a29daf553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"45\" style=\"vertical-align: -12px;\" \/><\/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-30dbbc4e285c24e3994612b614669318_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c3956ff9d64014e18ea7c005f596894_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#51;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/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-8cb19f193560276dc6b1b0dc8a9564a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-253ded36f0d00489c107ba70f3a75d12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#48;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/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-efa475690d66b7abd89bf957c7e994ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#97;&#125;&#94;&#123;&#49;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ecb407ed0b9ea01c462b78a5daf67ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#55;&#125;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"54\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9963adb67f276c79e876a56d94aa7f1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a24d7aad9c08b4951031e858064703e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#48;&#48;&#48;&#123;&#112;&#125;&#94;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/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-acf01ec288d493d761a291cd7fd711f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" 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-1b551e49534c4613f6fc87ba87e541fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#52;&#123;&#109;&#125;&#94;&#123;&#56;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" 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-53490834a64b46e349dbe9b14e481612_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#48;&#48;&#48;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">80. &#36;168.07<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">82.\u00a0Answers will vary.<\/td>\n<td style=\"width: 50%;\">84.\u00a0Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse Multiplication Properties of Exponents\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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","protected":false},"author":90,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1940","chapter","type-chapter","status-publish","hentry"],"part":1897,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1940","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\/1940\/revisions"}],"predecessor-version":[{"id":1941,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1940\/revisions\/1941"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/1897"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1940\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1940"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1940"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1940"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}