{"id":205,"date":"2021-06-23T01:01:04","date_gmt":"2021-06-23T01:01:04","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/integer-exponent-and-sn\/"},"modified":"2026-03-11T20:17:23","modified_gmt":"2026-03-11T20:17:23","slug":"integer-exponent-and-sn","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/integer-exponent-and-sn\/","title":{"raw":"1.5 Exponents and Scientific Notation","rendered":"1.5 Exponents and Scientific Notation"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section it is expected that you will be able to:\r\n<ul>\r\n \t<li>Simplify expressions with exponents<\/li>\r\n \t<li>Simplify expressions with zero exponents<\/li>\r\n \t<li>Use the definition of a negative exponent<\/li>\r\n \t<li>Use formulas with exponents in applications<\/li>\r\n \t<li>Convert from decimal notation to scientific notation<\/li>\r\n \t<li>Convert scientific notation to decimal form<\/li>\r\n \t<li>Multiply and divide using scientific notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Simplify Expressions with Exponents<\/h1>\r\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>\r\n<p id=\"fs-id1169597431995\">Let\u2019s review the vocabulary for expressions with exponents.<\/p>\r\n\r\n<div id=\"fs-id1169597500173\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exponential Notation (Power)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/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>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597488943\">This is read \\(a\\) to the \\({m}^{th}\\) power.<\/p>\r\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>\r\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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/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>\r\n\r\n<\/div>\r\n<p id=\"fs-id1169597357034\">Before we begin working with expressions containing exponents, let\u2019s simplify a few expressions involving only numbers.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597464503\" data-type=\"problem\">\r\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>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597379020\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-50\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\({4}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply three factors of 4.<\/td>\r\n<td>4 \u00b7 4 \u00b7 4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(64\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({7}^{1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply one factor of 7.<\/td>\r\n<td>\\(7\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c)<\/td>\r\n<td>\\({\\left(\\dfrac{5}{6}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply two factors.<\/td>\r\n<td>\\(\\left(\\dfrac{5}{6}\\right)\\left(\\dfrac{5}{6}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\dfrac{25}{36}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d)<\/td>\r\n<td>\\({\\left(0.63\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply two factors.<\/td>\r\n<td>\\(\\left(0.63\\right)\\left(0.63\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(0.3969\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597491698\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597497979\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597446527\" data-type=\"problem\">\r\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>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597342610\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597367714\">a) 216 b) \\(15\\) c) \\(\\dfrac{9}{49}\\) d) 0.1849<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597406059\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597531640\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597532637\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><a id=\"example2\"><\/a>EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597411906\" data-type=\"problem\">\r\n<p id=\"fs-id1169597497879\">Simplify: a) \\({\\left(-5\\right)}^{4}\\) b) \\(-{5}^{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597493725\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-539\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\({\\left(-5\\right)}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply four factors of \\(-5\\).<\/td>\r\n<td>\\(\\left(-5\\right)\\left(-5\\right)\\left(-5\\right)\\left(-5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(625\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\(-{5}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply four factors of 5.<\/td>\r\n<td>-(5\u00a0 \u00b7 5 \u00b7 5 \u00b7 5)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-625\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597444745\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597444745\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597350702\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597497219\" data-type=\"problem\">\r\n<p id=\"fs-id1169597415505\">Simplify: a) \\({\\left(-3\\right)}^{4}\\) b) \\(-{3}^{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597495810\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597537923\">a) \\(81\\) b) \\(-81\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597448020\">Notice the similarities and differences in <a class=\"autogenerated-content\" href=\"#example2\">(Example 2)<\/a> a) and <a class=\"autogenerated-content\" href=\"#example2\">(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>\r\n\r\n<div id=\"fs-id1169597397855\" data-type=\"note\"><img class=\"alignnone wp-image-6857\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/business-color_calculator_icon-icons.com_53466.png\" alt=\"\" width=\"18\" height=\"18\" \/> \u00a0When simplifying with exponents instead of multiplying the same factors, we can use scientific calculator and a key labelled<strong> <strong style=\"font-size: 18.6667px;\"> <img class=\"alignnone wp-image-6868\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.35.16-PM.png\" alt=\"\" width=\"30\" height=\"31\" \/> or <img class=\"alignnone wp-image-178\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.37.58-PM.png\" alt=\"\" width=\"28\" height=\"31\" \/> \u00a0<\/strong>.\u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0 \u00a0<\/strong><\/div>\r\n<div data-type=\"note\">For example, to find \\({\\left(0.7\\right)}^{5}\\), press: 0.7 <strong style=\"font-size: 18.6667px;\"><img class=\"alignnone wp-image-6868\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.35.16-PM.png\" alt=\"\" width=\"30\" height=\"31\" \/> <\/strong> 5\u00a0 <img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screen-Shot-2021-07-15-at-1.17.27-PM.png\" \/> .You should get 0.16807.<\/div>\r\n<div id=\"fs-id1169597490292\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><\/div>\r\n<h1>Simplify Expressions with an Exponent of Zero<\/h1>\r\nWhen simplifying expressions with exponents we very often use the <strong data-effect=\"bold\">Product Property and the Quotient Property.<\/strong>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Product Property for Exponents<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597491806\">If \\(a\\) is a real number, and \\(m\\) and \\(n\\) are counting numbers, then<\/p>\r\n\r\n<div id=\"fs-id1169597359735\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({a}^{m}\\cdot {a}^{n}={a}^{m+n}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597397855\" data-type=\"note\">\r\n<p id=\"fs-id1169597397229\">To multiply with like bases, add the exponents.<\/p>\r\n\r\n<\/div>\r\n<p id=\"fs-id1169597410476\">An example with numbers helps to verify this property.<\/p>\r\n\r\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>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596229342\">If \\(a\\) is a real number, \\(a\\ne 0\\), and \\(m\\) and \\(n\\) are whole numbers, then<\/p>\r\n\r\n<div id=\"fs-id1169596263364\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n},m\\) &gt; \\(n \\) and \\(\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{n-m}},n\\) &gt; \\(m\\)<\/div>\r\n<\/div>\r\n<\/div>\r\nA couple of examples with numbers may help to verify this property.\r\n\r\n\\(\\begin{array}{rlrl}\\dfrac{{3}^{4}}{{3}^{2}}&amp; = {3}^{4-2}\\hfill &amp; \\hfill \\dfrac{{5}^{2}}{{5}^{3}} &amp;= \\dfrac{1}{{5}^{3-2}} \\\\\u00a0 \\dfrac{81}{9} &amp;= {3}^{2}\\hfill &amp; \\dfrac{25}{125}&amp; = \\dfrac{1}{{5}^{1}} \\\\\u00a0 9&amp; = 9\\checkmark\\hfill &amp; \\dfrac{1}{5}&amp; = \\dfrac{1}{5}\\checkmark \\end{array}\\)\r\n<p id=\"fs-id1169596373087\">A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like \\(\\dfrac{{a}^{m}}{{a}^{m}}\\). From your earlier work with fractions, you know that:<\/p>\r\n\\(\\dfrac{2}{2}=1\u00a0 \\hspace{1cm} \\dfrac{17}{17}=1\u00a0 \\hspace{1cm} \\dfrac{-43}{-43}=1\\)\r\n<p id=\"fs-id1169596522381\">In words, a number divided by itself is 1. So, \\(\\dfrac{x}{x}=1\\), for any \\(x\\left(x\\ne 0\\right)\\), since any number divided by itself is 1<\/p>\r\n<p id=\"fs-id1169596522415\">The Quotient Property for Exponents shows us how to simplify \\(\\dfrac{{a}^{m}}{{a}^{n}}\\) when \\(m\\) &gt; \\(n\\) and when \\(n\\) &lt; \\(m\\) by subtracting exponents. What if \\(m=n\\)?<\/p>\r\n<p id=\"fs-id1169596362502\">Consider \\(\\frac{8}{8}\\), which we know is 1<\/p>\r\n\r\n<table id=\"eip-158\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\( \\dfrac{8}{8}=1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write \\(8\\) as \\({2}^{3}\\).<\/td>\r\n<td>\\(\\dfrac{{2}^{3}}{{2}^{3}}=1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract exponents.<\/td>\r\n<td>\\( {2}^{3-3}=1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\({2}^{0}=1\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169596534031\">Now we will simplify \\(\\dfrac{{a}^{m}}{{a}^{m}}\\) in two ways to lead us to the definition of the zero exponent. In general, for \\(a\\ne 0\\):<\/p>\r\n<span id=\"fs-id1169596534061\" data-type=\"media\" data-alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_05_005_img_new.jpg\" alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169596534074\">We see \\(\\dfrac{{a}^{m}}{{a}^{m}}\\) simplifies to \\({a}^{0}\\) and to 1. So \\({a}^{0}=1\\).<\/p>\r\n\r\n<div id=\"fs-id1169596531077\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Zero Exponent<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596531378\">If \\(a\\) is a non-zero number, then \\({a}^{0}=1\\).<\/p>\r\n<p id=\"fs-id1169596531400\">Any nonzero number raised to the zero power is 1<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><a id=\"example3\"><\/a>EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596531411\" data-type=\"problem\">\r\n<p id=\"fs-id1169596531413\">Simplify:\u00a0 \\({-9}^{0}\\) .<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596397936\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169596397941\">The definition says any non-zero number raised to the zero power is 1<\/p>\r\n\r\n<table id=\"eip-501\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Use the definition of the zero exponent.<\/td>\r\n<td>\\(\\begin{array}{c}{9}^{0}\\\\ 1\\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596529728\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596529731\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596529733\" data-type=\"problem\">\r\n<p id=\"fs-id1169596529735\">Simplify:\u00a0 \\({-1.5}^{0}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596533793\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596533796\">\u00a01<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nNow that we have defined the zero exponent, we can expand all the Properties of Exponents to include whole number exponents.\r\n<h1>Use the Definition of a Negative Exponent<\/h1>\r\n<p id=\"fs-id1169597357807\">\u00a0Now, let's use the definition of a <em data-effect=\"italics\">negative exponent <\/em>to simplify expressions<em data-effect=\"italics\">.<\/em><\/p>\r\n\r\n<div id=\"fs-id1169597337099\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Negative Exponent<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(n\\) is an integer and \\(a\\ne 0\\), then \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597576960\">The <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> tells us we can re-write the expression by taking the reciprocal of the base and then changing the sign of the exponent.<\/p>\r\n<p id=\"fs-id1169597478894\">Any expression that has negative exponents is not considered to be in simplest form. We will use the definition of a <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> and other properties of exponents to write the expression with only positive exponents.<a id=\"example4\"><\/a><\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597358215\" data-type=\"problem\">\r\n<p id=\"fs-id1169597383767\">Simplify: a) \\({4}^{-2}\\) b) \\({10}^{-3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597393699\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-426\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\({4}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{4}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{16}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({10}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{10}^{3}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{1000}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\r\n<p id=\"fs-id1169597341315\">Simplify: a) \\({2}^{-3}\\) b) \\({10}^{-7}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597541824\">a) \\(\\frac{1}{8}\\) b) \\(\\frac{1}{{10}^{7}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597339847\">In <a class=\"autogenerated-content\" href=\"#example4\">(Example 4)<\/a> we raised an integer to a negative exponent. What happens when we raise a fraction to a negative exponent? We\u2019ll start by looking at what happens to a fraction whose numerator is one and whose denominator is an integer raised to a negative exponent.<\/p>\r\n\r\n<table id=\"eip-532\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{1}{{a}^{\\-n}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{\\frac{1}{{a}^{n}}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the complex fraction.<\/td>\r\n<td>\\(1\\cdot\\frac{{a}^{n}}{1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>\\({a}^{n}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169597484548\">This leads to the Property of Negative Exponents.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Property of Negative Exponents<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(n\\) is an integer and \\(a\\ne 0\\), then \\(\\frac{1}{{a}^{-n}}={a}^{n}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597577846\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597529407\" data-type=\"problem\">\r\n\r\nSimplify: \\(\\frac{1}{{3}^{-2}}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597395509\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-453\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{1}{{3}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the property of a negative exponent, \\(\\frac{1}{{a}^{-n}}={a}^{n}\\).<\/td>\r\n<td>\\({3}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(9\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597467255\" data-type=\"problem\">\r\n<p id=\"fs-id1169597527634\">Simplify: \\(\\frac{1}{{4}^{-3}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597500869\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597465620\">\u00a0\\(64\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597393899\">Suppose now we have a fraction raised to a negative exponent. Let\u2019s use our definition of negative exponents to lead us to a new property.<\/p>\r\n\r\n<table id=\"eip-239\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\({\\left(\\frac{3}{4}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{\\left(\\frac{3}{4}\\right)}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the denominator.<\/td>\r\n<td>\\(\\frac{1}{\\frac{9}{16}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the complex fraction.<\/td>\r\n<td>\\(\\frac{16}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>But we know that \\(\\frac{16}{9}\\) is \\({\\left(\\frac{4}{3}\\right)}^{2}\\).<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>This tells us that:<\/td>\r\n<td>\\({\\left(\\frac{3}{4}\\right)}^{-2}={\\left(\\frac{4}{3}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169597409988\">To get from the original fraction raised to a negative exponent to the final result, we took the reciprocal of the base\u2014the fraction\u2014and changed the sign of the exponent.<\/p>\r\n<p id=\"fs-id1169597515519\">This leads us to the <em data-effect=\"italics\">Quotient to a Negative Power Property<\/em>.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Quotient to a Negative Exponent Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(a\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b\\) are real numbers, \\(a\\ne 0,b\\ne 0\\), and \\(n\\) is an integer, then \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597416290\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577456\" data-type=\"problem\">\r\n<p id=\"fs-id1169597492476\">Simplify:\u00a0 \\({\\left(\\frac{5}{7}\\right)}^{-2}\\) .<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597580588\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-116\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 700.868px;\"><\/td>\r\n<td style=\"width: 228.646px;\">\\({\\left(\\frac{5}{7}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 700.868px;\">Use the Quotient to a Negative Exponent Property, \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\).<\/td>\r\n<td style=\"width: 228.646px;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 700.868px;\">Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\r\n<td style=\"width: 228.646px;\">\\({\\left(\\frac{7}{5}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 700.868px;\">Simplify.<\/td>\r\n<td style=\"width: 228.646px;\">\\(\\frac{49}{25}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597520921\" data-type=\"problem\">\r\n<p id=\"fs-id1169597467530\">Simplify:\u00a0 \\({\\left(\\frac{2}{3}\\right)}^{-4}\\) .<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597540982\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597507465\">\u00a0\\(\\frac{81}{16}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597422172\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597533646\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\r\n\r\nWhen simplifying an expression with exponents, we must be careful to correctly identify the base.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597540378\" data-type=\"problem\">\r\n<p id=\"fs-id1169597703489\">Simplify: a) \\({\\left(-3\\right)}^{-2}\\) b) \\(-{3}^{-2}\\) c) \\({\\left(-\\frac{1}{3}\\right)}^{-2}\\) d) \\(-{\\left(\\frac{1}{3}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597467914\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-407\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a) Here the exponent applies to the base \\(-3\\).<\/td>\r\n<td>\\({\\left(-3\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(\\frac{1}{{\\left(-3\\right)}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b) The expression \\(-{3}^{-2}\\) means \"find the opposite of \\({3}^{-2}\\).\" Here the exponent applies to the base \\({\\left(-\\frac{1}{3}\\right)}^{}\\).<\/td>\r\n<td>\\(-{3}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a product with \\(-1\\).<\/td>\r\n<td>\\(-1\\cdot{3}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(-1\\cdot\\frac{1}{{3}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-\\frac{1}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c) Here the exponent applies to the base \\({\\left(-\\frac{1}{3}\\right)}^{}\\).<\/td>\r\n<td>\\({\\left(-\\frac{1}{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\({\\left(-\\frac{3}{1}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(9\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d) The expression \\(-{\\left(\\frac{1}{3}\\right)}^{-2}\\) means \"find the opposite of \\({\\left(\\frac{1}{3}\\right)}^{-2}\\).\" Here the exponent applies to the base \\(\\left(\\frac{1}{3}\\right)\\).<\/td>\r\n<td>\\(\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a product with \\(-1\\).<\/td>\r\n<td>\\(-1\\cdot{\\left(\\frac{1}{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(-1\\cdot{\\left(\\frac{3}{1}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-9\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597457044\" data-type=\"problem\">\r\n<p id=\"fs-id1169597457046\">Simplify: a) \\({\\left(-5\\right)}^{-2}\\) b) \\(-{5}^{-2}\\) c) \\({\\left(-\\frac{1}{5}\\right)}^{-2}\\) d) \\(-{\\left(\\frac{1}{5}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597577197\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597577199\">a) \\(\\frac{1}{25}\\) b) \\(-\\frac{1}{25}\\) c) 25 d) \\(-25\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597533353\">We must be careful to follow the Order of Operations. In the next example, parts (a) and (b) look similar, but the results are different.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597492583\" data-type=\"problem\">\r\n<p id=\"fs-id1169597492586\">Simplify: a) \\(4\\cdot{2}^{-1}\\) b) \\({\\left(4\\cdot 2\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597684591\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-779\" style=\"width: 100%;\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td>a)\r\nDo exponents before multiplication.<\/td>\r\n<td>\\(4\\cdot{2}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(4\\cdot\\frac{1}{{2}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(2\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({\\left(4\\cdot 2\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside the parentheses first.<\/td>\r\n<td>\\({\\left(8\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{8}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{8}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597479266\" data-type=\"problem\">\r\n<p id=\"fs-id1169597689696\">Simplify: a) \\(6\\cdot{3}^{-1}\\) b) \\({\\left(6\\cdot3\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597576993\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597576996\">a) \\(2\\) b) \\(\\frac{1}{18}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Use Formulas with Exponents in Applications<\/h1>\r\n<p id=\"fs-id1931140\">In this section, we will use geometry formulas that contain exponents to solve problems. Since we will be solving applications, we will once again show our Problem-Solving Strategy for Geometry Applications.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Problem Solving Strategy for Geometry Applications<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol class=\"stepwise\" type=\"1\">\r\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\r\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\r\n \t<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\r\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"CNX_BMath_Figure_09_06_001\" class=\"bc-figure figure\">\r\n<div id=\"CNX_BMath_Figure_09_06_002\" class=\"bc-figure figure\">\r\n<p id=\"fs-id1171505481979\">A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, <em data-effect=\"italics\">s<\/em> for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:<\/p>\r\n\\(\\begin{array}{ccccc}V=LWH\\hfill &amp; &amp; &amp; &amp; S=2LH+2LW+2WH\\hfill \\\\ V=\\text{s}\\cdot\\text{s}\\cdot\\text{s}\\hfill &amp; &amp; &amp; &amp; S=2\\text{s}\\cdot\\text{s}+2\\text{s}\\cdot\\text{s}+2\\text{s}\\cdot\\text{s}\\hfill \\\\ V={\\text{s}}^{3}\\hfill &amp; &amp; &amp; &amp; S=2{s}^{2}+2{s}^{2}+2{s}^{2}\\hfill \\\\ &amp; &amp; &amp; &amp; S=6{s}^{2}\\hfill \\end{array}\\)\r\n<p id=\"fs-id1767806\">So for a cube, the formulas for volume and surface area are \\(V={s}^{3}\\) and \\(S=6{s}^{2}\\).<\/p>\r\n\r\n<div id=\"fs-id1560075\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Volume and Surface Area of a Cube<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1516282\">For any cube with sides of length \\(s\\),<\/p>\r\n<span id=\"fs-id1171496258265\" data-type=\"media\" data-alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_010_img.jpg\" alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1171496189268\" data-type=\"problem\">\r\n<p id=\"fs-id1171505620889\">A cube is \\(2.5\\) inches on each side. Find its a) volume and b) surface area.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1585408\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1784097\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\r\n\r\n<table id=\"eip-id1168466154480\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2.5 by 2.5 by 2.5.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\r\nlabel it with the given information.<\/td>\r\n<td><span id=\"eip-id1168469766852\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_040_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168465993815\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the cube<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(V={s}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\r\n<td>\\(V={\\left(2.5\\right)}^{3}\\)\r\n\\(V=15.625\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check your work.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The volume is 15.625 cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466275896\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>b)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the cube<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(S=6{s}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\r\n<td>\\(S=6\\cdot {\\left(2.5\\right)}^{2}\\)\r\n\\(S=37.5\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The surface area is 37.5 square inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1489297\" data-type=\"problem\">\r\n<p id=\"fs-id1529247\">For a cube with side 4.5 metres, find the a) volume and b) surface area of the cube.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1933234\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<ol id=\"eip-id1168466248223\" class=\"circled\" type=\"a\">\r\n \t<li>91.125 cu. m<\/li>\r\n \t<li>121.5 sq. m<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1452349\" data-type=\"exercise\"><\/div>\r\n<\/div>\r\n<div id=\"fs-id1590812\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1418268\" data-type=\"exercise\">\r\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1171506138160\" data-type=\"problem\">\r\n<p id=\"fs-id1171505934498\">A notepad cube measures \\(2\\) inches on each side. Find its a) volume and b) surface area.<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168467296950\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2 by 2 by 2.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\r\nlabel it with the given information.<\/td>\r\n<td><span id=\"eip-id1168467496838\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_041_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467188434\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the cube<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(V={s}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\r\n<td>\\(V={2}^{3}\\)\r\n\\(V=8\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check that you did the calculations\r\ncorrectly.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The volume is 8 cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468478236\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>b)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the cube<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(S=6{s}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\r\n<td>\\(S=6\\cdot {2}^{2}\\)\r\n\\(S=24\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The surface area is 24 square inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1927378\" data-type=\"problem\">\r\n<p id=\"fs-id1871924\">A packing box is a cube measuring \\(4\\) feet on each side. Find its a) volume and b) surface area.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1171511527503\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\r\n \t<li>64 cu. ft<\/li>\r\n \t<li>96 sq. ft<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1038661\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id2058174\" data-type=\"exercise\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1954343\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\r\n<p id=\"eip-745\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate \\(\\pi \\) with \\(3.14\\).<\/p>\r\n\r\n<div id=\"fs-id1171512117057\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Volume and Surface Area of a Sphere<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1171512117850\">For a sphere with radius \\(r\\text{:}\\)<\/p>\r\n<span id=\"fs-id1171505277582\" data-type=\"media\" data-alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_015.jpg\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1171498454044\" data-type=\"problem\">\r\n<p id=\"fs-id1171498401975\">A sphere has a radius \\(6\\) inches. Find its a) volume and b) surface area.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1650050\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1171512511594\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\r\n\r\n<table id=\"eip-id1168468504255\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a sphere. The radius is labeled 6.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label\r\nit with the given information.<\/td>\r\n<td><span id=\"eip-id1168468504279\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466046693\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the sphere<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(V=\\frac{4}{3}\\pi {r}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\r\n<td>\\(V\\approx \\frac{4}{3}\\left(3.14\\right){6}^{3}\\)\r\n\\(V\\approx 904.32\\phantom{\\rule{0.2em}{0ex}}\\text{cubic inches}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The volume is approximately 904.32 cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467263246\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>b)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the cube<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td>\\(S=4\\pi {r}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\r\n<td>\\(S\\approx 4\\left(3.14\\right){6}^{2}\\)\r\n\\(S\\approx 452.16\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The surface area is approximately 452.16 square inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1913002\" data-type=\"problem\">\r\n<p id=\"fs-id1171488074403\">Find the a) volume and b) surface area of a sphere with radius 3 centimetres.<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<ol id=\"eip-id1168466006411\" class=\"circled\" type=\"a\">\r\n \t<li>113.04 cu. cm<\/li>\r\n \t<li>113.04 sq. cm<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1171506644186\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id2091579\" data-type=\"exercise\"><\/div>\r\n<\/div>\r\n<div id=\"fs-id1171498000511\" class=\"try\" data-type=\"note\">\r\n<div data-type=\"exercise\">\r\n<div id=\"fs-id748315\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id945308\" data-type=\"problem\">\r\n<p id=\"fs-id1566505\">A globe of Earth is in the shape of a sphere with radius \\(14\\) centimetres. Find its a) volume and b) surface area. Round the answer to the nearest hundredth.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1171488252639\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168467368787\" style=\"width: 100%;\" summary=\"Step 1. Read the problem.\u201d Beside this is an image of a globe. The radius is labeled 14.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw a figure with the\r\ngiven information and label it.<\/td>\r\n<td><span id=\"eip-id1168467309173\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168464926516\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the volume of the sphere<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.\r\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\r\n<td>\\(V=\\frac{4}{3}\\pi {r}^{3}\\)\r\n\\(V\\approx \\frac{4}{3}\\left(3.14\\right){14}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\r\n<td>\\(V\\approx 11,488.21\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The volume is approximately 11,488.21 cubic inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468466725\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>b)<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\r\n<td>the surface area of the sphere<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\r\nWrite the appropriate formula.\r\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\r\n<td>\\(S=4\\pi {r}^{2}\\)\r\n\\(S\\approx 4\\left(3.14\\right){14}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\r\n<td>\\(S\\approx 2461.76\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\r\n<td>The surface area is approximately 2461.76 square inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1561201\" data-type=\"problem\">\r\n<p id=\"fs-id1398847\">A beach ball is in the shape of a sphere with radius of \\(9\\) inches. Find its a) volume and b) surface area.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1531978\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<ol id=\"eip-id1168468772882\" class=\"circled\" type=\"a\">\r\n \t<li>3052.08 cu. in.<\/li>\r\n \t<li>1017.36 sq. in.<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1418575\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1398911\" data-type=\"exercise\"><\/div>\r\n<\/div>\r\n<h1>Convert from Decimal Notation to Scientific Notation<\/h1>\r\n<p id=\"fs-id1169597689470\">Remember working with place value for whole numbers and decimals? Our number system is based on powers of 10. We use tens, hundreds, thousands, and so on. Our decimal numbers are also based on powers of tens\u2014tenths, hundredths, thousandths, and so on. Consider the numbers 4,000 and \\(0.004\\). We know that 4,000 means \\(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}1,000\\) and 0.004 means \\(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1,000}\\).<\/p>\r\n<p id=\"fs-id1169597740645\">If we write the 1000 as a power of ten in exponential form, we can rewrite these numbers in this way:<\/p>\r\n\r\n<div id=\"fs-id1169597740648\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}4,000\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}0.004\\hfill \\\\ 4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}1,000\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1,000}\\hfill \\\\ 4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{{10}^{3}}\\hfill \\\\ &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169597742460\">When a number is written as a product of two numbers, where the first factor is a number greater than or equal to one but less than 10, and the second factor is a power of 10 written in exponential form, it is said to be in <em data-effect=\"italics\">scientific notation.<\/em><\/p>\r\n\r\n<div id=\"fs-id1169597742470\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Scientific Notation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597742475\">A number is expressed in scientific notation when it is of the form<\/p>\r\n\r\n<div id=\"fs-id1169597742489\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}&amp; &amp; &amp; a\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{n}\\phantom{\\rule{0.2em}{0ex}}\\text{where}\\phantom{\\rule{0.2em}{0ex}}1\\le a&lt;10\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}\\text{is an integer}\\hfill \\end{array}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597516025\">It is customary in scientific notation to use as the \\(\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\) multiplication sign, even though we avoid using this sign elsewhere in algebra.<\/p>\r\n<p id=\"fs-id1169597523393\">If we look at what happened to the decimal point, we can see a method to easily convert from decimal notation to <span class=\"no-emphasis\" data-type=\"term\">scientific notation<\/span>.<\/p>\r\n<span id=\"fs-id1169597523406\" data-type=\"media\" data-alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_002_img_new.jpg\" alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169597523423\">In both cases, the decimal was moved 3 places to get the first factor between 1 and 10<\/p>\r\n<p id=\"fs-id1169594046599\">\\(\\begin{array}{cccc}\\text{The power of 10 is positive when the number is larger than 1:}\\hfill &amp; &amp; &amp; 4,000=4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\hfill \\\\ \\text{The power of 10 is negative when the number is between 0 and 1:}\\hfill &amp; &amp; &amp; 0.004=4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\end{array}\\)<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Convert from Decimal Notation to Scientific Notation<\/div>\r\n<div id=\"fs-id1169597691148\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597691150\" data-type=\"problem\">\r\n<p id=\"fs-id1169597691152\">Write in scientific notation: 37,000.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597691157\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1169597691159\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.\u201d The second cell reads \u201cRemember, there is a decimal at the end of 37,000.\u201d The third cell contains 37,000. One line down, the second cell reads \u201cMove the decimal after the 3. 3.7000 is between 1 and 10.\u201d\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.\u201d The second cell reads \u201cRemember, there is a decimal at the end of 37,000.\u201d The third cell contains 37,000. One line down, the second cell reads \u201cMove the decimal after the 3. 3.7000 is between 1 and 10.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691266\" data-type=\"media\" data-alt=\"In the second row, the first cell reads \u201cStep 2. Count the number of decimal places, n, that the decimal place was moved. The second cell reads \u201cThe decimal point was moved 4 places to the left.\u201d The third cell contains 370000 again, with an arrow showing the decimal point jumping places to the left from the end of the number until it ends up between the 3 and the 7.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003b_img_new.jpg\" alt=\"In the second row, the first cell reads \u201cStep 2. Count the number of decimal places, n, that the decimal place was moved. The second cell reads \u201cThe decimal point was moved 4 places to the left.\u201d The third cell contains 370000 again, with an arrow showing the decimal point jumping places to the left from the end of the number until it ends up between the 3 and the 7.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691281\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Write the number as a product with a power of 10. If the original number is greater than 1, the power of 10 will be 10 to the n power. If it\u2019s between 0 and 1, the power of 10 will be 10 to the negative n power.\u201d The second cell reads \u201c37,000 is greater than 1, so the power of 10 will have exponent 4.\u201d The third cell contains 3.7 times 10 to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Write the number as a product with a power of 10. If the original number is greater than 1, the power of 10 will be 10 to the n power. If it\u2019s between 0 and 1, the power of 10 will be 10 to the negative n power.\u201d The second cell reads \u201c37,000 is greater than 1, so the power of 10 will have exponent 4.\u201d The third cell contains 3.7 times 10 to the fourth power.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691296\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Check.\u201d The second cell reads \u201cCheck to see if your answer makes sense.\u201d The third cell reads \u201c10 to the fourth power is 10,000 and 10,000 times 3.7 will be 37,000.\u201d Below this is 37,000 equals 3.7 times 10 to the fourth power.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Check.\u201d The second cell reads \u201cCheck to see if your answer makes sense.\u201d The third cell reads \u201c10 to the fourth power is 10,000 and 10,000 times 3.7 will be 37,000.\u201d Below this is 37,000 equals 3.7 times 10 to the fourth power.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597536011\" data-type=\"problem\">\r\n<p id=\"fs-id1169597536013\">Write in scientific notation: \\(96,000\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597536022\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597536024\">\\(9.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Convert from decimal notation to scientific notation<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1168743403951\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\r\n \t<li>Count the number of decimal places, <em data-effect=\"italics\">n<\/em>, that the decimal point was moved.<\/li>\r\n \t<li>Write the number as a product with a power of 10.\r\nIf the original number is:<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<ul id=\"fs-id1168744092452\" data-bullet-style=\"bullet\">\r\n \t<li>greater than 1, the power of 10 will be 10<sup><em data-effect=\"italics\">n<\/em><\/sup>.<\/li>\r\n \t<li>between 0 and 1, the power of 10 will be 10<sup><em data-effect=\"italics\">\u2212n<\/em><\/sup>.<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ul>\r\n<div id=\"fs-id1168743403943\" class=\"howto\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597701094\" data-type=\"problem\">\r\n<p id=\"fs-id1169597701096\">Write in scientific notation: \\(0.0052\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597701105\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169597701107\">The original number, \\(0.0052\\), is between 0 and 1 so we will have a negative power of 10<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 115px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 25px;\">\r\n<td style=\"width: 50%; height: 25px;\"><\/td>\r\n<td style=\"width: 50%; height: 25px;\"><span id=\"eip-id1172181050459\" data-type=\"media\" data-alt=\"0.0052.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004a_img_new.jpg\" alt=\"0.0052.\" width=\"110\" height=\"11\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">Move the decimal point to get 5.2, a number between 1 and 10.<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050475\" data-type=\"media\" data-alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004b_img_new.jpg\" alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\" width=\"119\" height=\"17\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">Count the number of decimal places the point was moved.<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050492\" data-type=\"media\" data-alt=\"3 places.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004c_img_new.jpg\" alt=\"3 places.\" width=\"118\" height=\"16\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">Write as a product with a power of 10.<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050509\" data-type=\"media\" data-alt=\"5.2 times 10 to the power of negative 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004d_img_new.jpg\" alt=\"5.2 times 10 to the power of negative 3.\" width=\"123\" height=\"12\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">Check.<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">\\(\\begin{array}{ccccc}\\\\ \\\\ \\phantom{\\rule{3em}{0ex}}5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\\\ \\phantom{\\rule{3em}{0ex}}5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{{10}^{3}}\\hfill \\\\ \\phantom{\\rule{3em}{0ex}}5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1000}\\hfill \\\\ \\phantom{\\rule{3em}{0ex}}5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}0.001\\hfill \\end{array}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">\\(\\phantom{\\rule{2em}{0ex}}0.0052\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577078\" data-type=\"problem\">\r\n<p id=\"fs-id1169597577080\">Write in scientific notation: \\(0.0078\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597577089\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597577091\">\\(7.8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Convert Scientific Notation to Decimal Form<\/h1>\r\n<p id=\"fs-id1169597555698\">How can we convert from scientific notation to decimal form? Let\u2019s look at two numbers written in scientific notation and see.<\/p>\r\n\r\n<div id=\"fs-id1169597555702\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\hfill \\\\ \\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}10,000\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}0.0001\\hfill \\\\ \\hfill 91,200\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}0.000912\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169597688301\">If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.<\/p>\r\n\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}=91,200\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}=0.000912\\hfill \\end{array}\\)<\/div>\r\n<span id=\"fs-id1169597742376\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_02_015_img.jpg\" alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169597742371\">In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Convert Scientific Notation to Decimal Form<\/div>\r\n<div id=\"fs-id1169597741743\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597741745\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741747\">Convert to decimal form: \\(6.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597741764\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1169597741774\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006a_img_new.jpg\" alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597741789\" data-type=\"media\" data-alt=\"In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006b_img_new.jpg\" alt=\"In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597741802\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597741410\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741412\">Convert to decimal form: \\(1.3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597741429\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597741431\">1,300<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597505408\">The steps are summarized below.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Convert scientific notation to decimal form.<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597505421\">To convert scientific notation to decimal form:<\/p>\r\n\r\n<ol id=\"fs-id1168746296183\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the exponent, \\(n\\), on the factor 10.<\/li>\r\n \t<li>Move the decimal \\(n\\) places, adding zeros if needed.\r\n<ul id=\"fs-id1169597505448\" data-bullet-style=\"bullet\">\r\n \t<li>If the exponent is positive, move the decimal point \\(n\\) places to the right.<\/li>\r\n \t<li>If the exponent is negative, move the decimal point \\(|n|\\) places to the left.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597505412\" class=\"howto\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597744324\" data-type=\"problem\">\r\n<p id=\"fs-id1169597744326\">Convert to decimal form: \\(8.9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597744344\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187383117\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, in the right column is 8.9 times 10 to the negative second power. One row down, the text in the left column says \u201cDetermine the exponent, n, on the factor 10.\u201d The right column says \u201cThe exponent is negative 2.\u201d One row down, the text in the left column says \u201cSince the exponent is negative, move the decimal point 2 places to the left.\u201d The right column contains 8.9, with an arrow showing the decimal point in 9.12 being moved two places to the left. Because there are no digits before 8, the remaining places are represented by spaces. One row down, the text in the left says \u201cAdd zeros as needed for placeholders.\u201d The right column contains 8.9 times 10 to the negative second power equals 0.089.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172187383136\" data-type=\"media\" data-alt=\"8.9 times 10 to the power of negative 2.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007a_img_new.jpg\" alt=\"8.9 times 10 to the power of negative 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the exponent, <em data-effect=\"italics\">n<\/em>, on the factor 10.<\/td>\r\n<td><span id=\"eip-id1172187383152\" data-type=\"media\" data-alt=\"The exponent is negative 2.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007b_img_new.jpg\" alt=\"The exponent is negative 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since the exponent is negative, move the decimal point 2 places to the left.<\/td>\r\n<td><span id=\"eip-id1172187383169\" data-type=\"media\" data-alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007c_img_new.jpg\" alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add zeros as needed for placeholders.<\/td>\r\n<td><span id=\"eip-id1172187383201\" data-type=\"media\" data-alt=\"8.9 times 10 to the power of negative 2 equals 0.089.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007e_img_new.jpg\" alt=\"8.9 times 10 to the power of negative 2 equals 0.089.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597739737\" data-type=\"problem\">\r\n<p id=\"fs-id1169597739739\">Convert to decimal form: \\(1.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597739758\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597739760\">0.00012<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Multiply and Divide Using Scientific Notation<\/h1>\r\n<p id=\"fs-id1169597704318\">Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\r\n<p id=\"fs-id1169597704332\">Multiply. Write answers in decimal form: \\(\\left(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{5}\\right)\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-7}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\"><\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\left(4\\times{10}^{5}\\right)\\left(2\\times{10}^{-7}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Use the Commutative Property to rearrange the factors.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(4\\cdot 2\\cdot{10}^{5}\\cdot{10}^{-7}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Multiply.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(8\\times{10}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Change to decimal form by moving the decimal two places left.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(0.08\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597576869\" data-type=\"problem\">\r\n<p id=\"fs-id1169597576871\">Multiply \\(\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}\\right)\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-8}\\right)\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597533136\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597533139\">0.06<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597576863\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597576867\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\r\n<p id=\"fs-id1169597704332\">Multiply. Write answer in scientific notation: \\(\\left(3.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\right)\\left(6.3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\"><\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\left(3.2\\times{10}^{-3}\\right)\\left(6.3\\times{10}^{9}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Use the Commutative Property to rearrange the factors.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(3.2\\cdot 6.3\\cdot{10}^{-3}\\cdot{10}^{9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Multiply.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(20.16\\times{10}^{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Write the answer in scientific notation.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(2.016\\times{10}^{7}\\)\r\n\r\n&nbsp;<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\r\n<p id=\"fs-id1169597539395\">Multiply. Write answer in scientific notation: \\(\\left(2.7\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\right)\\left(7.9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597539428\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\\(2.133\\times{10}^{-2}\\)\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\r\n<p id=\"fs-id1169597705347\">Divide. Write answers in decimal form: \\(\\frac{9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}}{3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">\\(\\frac{9\\times{10}^{3}}{3\\times{10}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Separate the factors, rewriting as the product of two fractions.<\/td>\r\n<td style=\"width: 50%;\">\\(\\frac{9}{3}\\times\\frac{{10}^{3}}{{10}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Divide.<\/td>\r\n<td style=\"width: 50%;\">\u00a0\\(3\\times{10}^{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Change to decimal form by moving the decimal five places right.<\/td>\r\n<td style=\"width: 50%;\">\u00a0\\(300,000\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\r\n<p id=\"fs-id1169597539395\">Divide \\(\\frac{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}}{2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}}\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597539428\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597539431\">400,000<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597533145\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597533149\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597705332\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\r\n<p id=\"fs-id1169597705347\">Divide. Write answer in scientific notation: \\(\\frac{3.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}}{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">\\(\\frac{3.2\\times{10}^{4}}{8\\times{10}^{-5}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Separate the factors, rewriting as the product of two fractions.<\/td>\r\n<td style=\"width: 50%;\">\\(\\frac{3.2}{8}\\times\\frac{{10}^{4}}{{10}^{-5}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Divide.<\/td>\r\n<td style=\"width: 50%;\">\u00a0\\(0.4\\times{10}^{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Write answer in scientific notation<\/td>\r\n<td style=\"width: 50%;\">\u00a0\\(4\\times{10}^8\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\r\n<p id=\"fs-id1169597539395\">Divide \\(\\frac{2.585\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{5}}{3.8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}}\\). Write answer in scientific notation.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597539428\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597539431\">\\(6.8\\times{10}^3\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nAccess these online resources for additional instruction and practice with integer exponents and scientific notation:\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597739988\" class=\"media-2\" data-type=\"note\">\r\n<ul id=\"fs-id1169597739997\" data-display=\"block\">\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Negexponents\">Negative Exponents<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot1\">Scientific Notation<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot2\">Scientific Notation 2<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1169597688248\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Exponential Notation<\/strong>\r\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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/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>\r\n \t<li><strong data-effect=\"bold\">Product Property of Exponents<\/strong>\r\n<ul id=\"fs-id1169597506748\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(a,b\\) are real numbers and \\(m,n\\) are whole numbers, then\r\n\\(\\ {a}^{m}\\cdot {a}^{n}&amp; =\u00a0 {a}^{m+n} \\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<ul id=\"fs-id1169597689120\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Quotient Property for Exponents:<\/strong>\r\n<ul id=\"fs-id1169596530872\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(a\\) is a real number, \\(a\\ne 0\\), and \\(m,n\\) are whole numbers, then:\r\n\\(\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n},m\\) &gt; \\(n\\text{ and }\\dfrac{{a}^{m}}{{a}^{n}}=\\dfrac{1}{{a}^{m-n}},n\\) &gt; \\(m\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Zero Exponent<\/strong>\r\n<ul id=\"fs-id1169596398934\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(a\\) is a non-zero number, then \\({a}^{0}=1\\).<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Property of Negative Exponents<\/strong>\r\n<ul id=\"fs-id1169597689133\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(n\\) is a positive integer and \\(a\\ne 0\\), then \\(\\frac{1}{{a}^{-n}}={a}^{n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Quotient to a Negative Exponent<\/strong>\r\n<ul id=\"fs-id1169597689185\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(a,b\\) are real numbers, \\(b\\ne 0\\) and \\(n\\) is an integer , then \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">To convert a decimal to scientific notation:<\/strong>\r\n<ol id=\"fs-id1168746309069\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\r\n \t<li>Count the number of decimal places, \\(n\\), that the decimal point was moved.<\/li>\r\n \t<li>Write the number as a product with a power of 10. If the original number is:\r\n<ul id=\"fs-id1169596704515\" data-bullet-style=\"open-circle\">\r\n \t<li>greater than 1, the power of 10 will be \\({10}^{n}\\)<\/li>\r\n \t<li>between 0 and 1, the power of 10 will be \\({10}^{-n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">To convert scientific notation to decimal form:<\/strong>\r\n<ol id=\"fs-id1168744116887\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the exponent, \\(n\\), on the factor 10.<\/li>\r\n \t<li>Move the decimal \\(n\\)places, adding zeros if needed.\r\n<ul id=\"fs-id1169597742509\" data-bullet-style=\"open-circle\">\r\n \t<li>If the exponent is positive, move the decimal point \\(n\\) places to the right.<\/li>\r\n \t<li>If the exponent is negative, move the decimal point \\(|n|\\) places to the left.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h1>1.5 Exercise Set<\/h1>\r\n<p id=\"fs-id1168745177173\">In the following exercises, simplify each expression with exponents.<\/p>\r\n\r\n<ol class=\"twocolumn\">\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({3}^{5}\\)<\/li>\r\n \t<li>\\({9}^{1}\\)<\/li>\r\n \t<li>\\({\\left(\\dfrac{1}{3}\\right)}^{2}\\)<\/li>\r\n \t<li>\\({\\left(0.2\\right)}^{4}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({2}^{6}\\)<\/li>\r\n \t<li>\\({14}^{1}\\)<\/li>\r\n \t<li>\\({\\left(\\dfrac{2}{5}\\right)}^{3}\\)<\/li>\r\n \t<li>\\({\\left(0.7\\right)}^{2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({\\left(-6\\right)}^{4}\\)<\/li>\r\n \t<li>\\(-{6}^{4}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(-{\\left(\\dfrac{2}{3}\\right)}^{2}\\)<\/li>\r\n \t<li>\\({\\left(-\\dfrac{2}{3}\\right)}^{2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(-{0.5}^{2}\\)<\/li>\r\n \t<li>\\({\\left(-0.5\\right)}^{2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\nIn the following exercises, simplify.\r\n<ol class=\"twocolumn\" start=\"6\">\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({20}^{0}\\)<\/li>\r\n \t<li>\\({b}^{0}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({\\left(-27\\right)}^{0}\\)<\/li>\r\n \t<li>\\(-\\left({27}^{0}\\right)\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\nIn the following exercises, simplify.\r\n<ol class=\"twocolumn\" start=\"8\">\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({3}^{-4}\\)<\/li>\r\n \t<li>\\({10}^{-2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({2}^{-8}\\)<\/li>\r\n \t<li>\\({(-10)}^{-2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\\(\\frac{1}{{5}^{-2}}\\)<\/li>\r\n \t<li>\u00a0\\(\\frac{1}{{10}^{-4}}\\)<\/li>\r\n \t<li>\u00a0\\({\\left(\\frac{3}{10}\\right)}^{-2}\\)<\/li>\r\n \t<li>\\({\\left(\\frac{7}{2}\\right)}^{-3}\\)<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\({\\left(-7\\right)}^{-2}\\)<\/li>\r\n \t<li>\\(-{7}^{-2}\\)<\/li>\r\n \t<li>\\({\\left(-\\frac{1}{7}\\right)}^{-2}\\)<\/li>\r\n \t<li>\\(-{\\left(\\frac{1}{7}\\right)}^{-2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(-{5}^{-3}\\)<\/li>\r\n \t<li>\\({\\left(-\\frac{1}{5}\\right)}^{-3}\\)<\/li>\r\n \t<li>\\(-{\\left(\\frac{1}{5}\\right)}^{-3}\\)<\/li>\r\n \t<li>\\({\\left(-5\\right)}^{-3}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(2\\cdot{5}^{-1}\\)<\/li>\r\n \t<li>\\({\\left(2\\cdot 5\\right)}^{-1}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(3\\cdot{4}^{-2}\\)<\/li>\r\n \t<li>\\({\\left(3\\cdot 4\\right)}^{-2}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\nIn the following exercises, find a) the volume and b) the surface area of the cube with the given side length.\r\n<ol class=\"twocolumn\" start=\"18\">\r\n \t<li>\\(5\\) centimetres<\/li>\r\n \t<li>\\(10.4\\) feet<\/li>\r\n<\/ol>\r\nIn the following exercises, solve.\r\n<ol start=\"20\">\r\n \t<li><strong data-effect=\"bold\">Museum<\/strong> A cube-shaped museum has sides \\(64\\) metres long. Find its a) volume and b) surface area.<\/li>\r\n \t<li><strong data-effect=\"bold\">Base of statue<\/strong> The base of a statue is a cube with sides \\(2.8\\) metres long. Find its a) volume and b) surface area.<\/li>\r\n<\/ol>\r\nIn the following exercises, find a) the volume and b) the surface area of the sphere with the given radius. Round answers to the nearest hundredth.\r\n<ol class=\"twocolumn\" start=\"22\">\r\n \t<li>\\(3\\) centimetres<\/li>\r\n \t<li>\\(7.5\\) feet<\/li>\r\n<\/ol>\r\nIn the following exercises, solve. Round answers to the nearest hundredth.\r\n<ol start=\"24\">\r\n \t<li><strong data-effect=\"bold\">Exercise ball<\/strong> An exercise ball has a radius of \\(15\\) inches. Find its a) volume and b) surface area.<\/li>\r\n \t<li><strong data-effect=\"bold\">Golf ball<\/strong> A golf ball has a radius of \\(4.5\\) centimetres. Find its a) volume and b) surface area.<\/li>\r\n<\/ol>\r\nIn the following exercises, write each number in scientific notation.\r\n<ol class=\"twocolumn\" start=\"26\">\r\n \t<li>340,000<\/li>\r\n \t<li>1,290,000<\/li>\r\n \t<li>0.041<\/li>\r\n \t<li>0.00000103<\/li>\r\n<\/ol>\r\nIn the following exercises, convert each number to decimal form.\r\n<ol class=\"twocolumn\" start=\"30\">\r\n \t<li>\\(8.3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}\\)<\/li>\r\n \t<li>\\(1.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{10}\\)<\/li>\r\n \t<li>\\(3.8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/li>\r\n \t<li>\\(1.93\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\)<\/li>\r\n<\/ol>\r\nIn the following exercises, multiply. Write your answer in decimal form.\r\n<ol class=\"twocolumn\" start=\"34\">\r\n \t<li>\\(\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}\\right)\\left(1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\right)\\)<\/li>\r\n \t<li>\\(\\left(3.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\right)\\left(1.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\right)\\)<\/li>\r\n<\/ol>\r\nIn the following exercises, divide. Write your answer in decimal form.\r\n<ol start=\"36\">\r\n \t<li>\\(\\frac{5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}{1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-10}}\\)<\/li>\r\n \t<li>\\(\\frac{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}}{4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}}\\)<\/li>\r\n \t<li>The population of the world on July 1, 2010 was more than 6,850,000,000. Write the number in scientific notation<\/li>\r\n \t<li>The probability of winning the lottery was about 0.0000000057. Write the number in scientific notation.<\/li>\r\n \t<li>The width of a proton is \\(1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\) of the width of an atom. Convert this number to decimal form.<\/li>\r\n \t<li><strong data-effect=\"bold\">Coin production<\/strong> In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.<\/li>\r\n \t<li><strong>Debt<\/strong> At the end of fiscal year 2019 the gross Canadian federal government debt was estimated to be approximately \\$685,450,000,000 (\\$685.45 billion), according to the Federal Budget. The population of Canada was approximately 37,590,000 people at the end of fiscal year 2019.\r\n<ol type=\"a\">\r\n \t<li>Write the debt in scientific notation.<\/li>\r\n \t<li>Write the population in scientific notation.<\/li>\r\n \t<li>Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h1>Answers:<\/h1>\r\n<ol class=\"twocolumn\">\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>243<\/li>\r\n \t<li>9<\/li>\r\n \t<li>\\(\\frac{1}{9}\\)<\/li>\r\n \t<li>0.0016<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>64<\/li>\r\n \t<li>14<\/li>\r\n \t<li>\\(\\frac{8}{125}\\)<\/li>\r\n \t<li>0.49<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>1296<\/li>\r\n \t<li>\u22121296<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(-\\frac{4}{9}\\)<\/li>\r\n \t<li>\\(\\frac{4}{9}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\u22120.25<\/li>\r\n \t<li>0.25<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>1<\/li>\r\n \t<li>1<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>1<\/li>\r\n \t<li>\u22121<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\frac{1}{81}\\)<\/li>\r\n \t<li>\\(\\frac{1}{100}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\frac{1}{256}\\)<\/li>\r\n \t<li>\\(\\frac{1}{100}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>25<\/li>\r\n \t<li>10000<\/li>\r\n \t<li>\\(\\frac{100}{9}\\)<\/li>\r\n \t<li>\\(\\frac{8}{343}\\)<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\frac{1}{49}\\)<\/li>\r\n \t<li>\\(-\\frac{1}{49}\\)<\/li>\r\n \t<li>49<\/li>\r\n \t<li>\\(-49\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(-\\frac{1}{125}\\)<\/li>\r\n \t<li>\\(-125\\)<\/li>\r\n \t<li>\\(-125\\)<\/li>\r\n \t<li>\\(-\\frac{1}{125}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\frac{2}{5}\\)<\/li>\r\n \t<li>\\(\\frac{1}{10}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\frac{3}{16}\\)<\/li>\r\n \t<li>\\(\\frac{1}{144}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>125 cu. cm<\/li>\r\n \t<li>150 sq. cm<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>1124.864 cu. ft.<\/li>\r\n \t<li>648.96 sq. ft<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>262,144 cu. ft<\/li>\r\n \t<li>24,576 sq. ft<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>21.952 cu. m<\/li>\r\n \t<li>47.04 sq. m<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>113.04 cu. cm<\/li>\r\n \t<li>113.04 sq. cm<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>1,766.25 cu. ft<\/li>\r\n \t<li>706.5 sq. ft<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>14,130 cu. in.<\/li>\r\n \t<li>2,826 sq. in.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>381.51 cu. cm<\/li>\r\n \t<li>254.34 sq. cm<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\\(3.4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{5}\\)<\/li>\r\n \t<li>\\(1.29\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}\\)<\/li>\r\n \t<li>\\(4.1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/li>\r\n \t<li>\\(1.03\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\)<\/li>\r\n \t<li>830<\/li>\r\n \t<li>16,000,000,000<\/li>\r\n \t<li>0.038<\/li>\r\n \t<li>0.0000193<\/li>\r\n \t<li>0.02<\/li>\r\n \t<li>\\(5.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\)<\/li>\r\n \t<li>500,000,000<\/li>\r\n \t<li>20,000,000<\/li>\r\n \t<li>\\(6.85\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\)<\/li>\r\n \t<li>\\(5.7\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-10}\\)<\/li>\r\n \t<li>0.00001<\/li>\r\n \t<li>\\(1.545\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\)<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(6.8545\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{11}\\)<\/li>\r\n \t<li>\\(3.759\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{7}\\)<\/li>\r\n \t<li>\\(1.823\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cInteger Exponents and Scientific Notation\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","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 it is expected that you will be able to:<\/p>\n<ul>\n<li>Simplify expressions with exponents<\/li>\n<li>Simplify expressions with zero exponents<\/li>\n<li>Use the definition of a negative exponent<\/li>\n<li>Use formulas with exponents in applications<\/li>\n<li>Convert from decimal notation to scientific notation<\/li>\n<li>Convert scientific notation to decimal form<\/li>\n<li>Multiply and divide using scientific notation<\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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 (Power)<\/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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/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 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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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<\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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 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\"><a id=\"example2\"><\/a>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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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<\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597448020\">Notice the similarities and differences in <a class=\"autogenerated-content\" href=\"#example2\">(Example 2)<\/a> a) and <a class=\"autogenerated-content\" href=\"#example2\">(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\/businesstechnicalmath\/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<div id=\"fs-id1169597397855\" data-type=\"note\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6857\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/business-color_calculator_icon-icons.com_53466.png\" alt=\"\" width=\"18\" height=\"18\" \/> \u00a0When simplifying with exponents instead of multiplying the same factors, we can use scientific calculator and a key labelled<strong> <strong style=\"font-size: 18.6667px;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6868\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.35.16-PM.png\" alt=\"\" width=\"30\" height=\"31\" \/> or <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-178\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.37.58-PM.png\" alt=\"\" width=\"28\" height=\"31\" srcset=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.37.58-PM.png 80w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.37.58-PM-65x72.png 65w\" sizes=\"auto, (max-width: 28px) 100vw, 28px\" \/> \u00a0<\/strong>.\u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0 \u00a0<\/strong><\/div>\n<div data-type=\"note\">For example, to find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-39a074415f7ff4a38a187f9592d597ab_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;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -5px;\" \/>, press: 0.7 <strong style=\"font-size: 18.6667px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6868\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/Screen-Shot-2021-07-15-at-1.35.16-PM.png\" alt=\"\" width=\"30\" height=\"31\" \/> <\/strong> 5\u00a0 <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screen-Shot-2021-07-15-at-1.17.27-PM.png\" alt=\"image\" \/> .You should get 0.16807.<\/div>\n<div id=\"fs-id1169597490292\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><\/div>\n<h1>Simplify Expressions with an Exponent of Zero<\/h1>\n<p>When simplifying expressions with exponents we very often use the <strong data-effect=\"bold\">Product Property and the Quotient Property.<\/strong><\/p>\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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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 id=\"fs-id1169597397855\" data-type=\"note\">\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\/businesstechnicalmath\/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 class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596229342\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a real number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> are whole numbers, then<\/p>\n<div id=\"fs-id1169596263364\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d388c5467ca8f0ee93f59d2cca11eaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dc33298a92b30a494ba4671aff7425b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#45;&#109;&#125;&#125;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/div>\n<\/div>\n<p>A couple of examples with numbers may help to verify this property.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ccdcdaccdfbd05d9cf609f7177900e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#108;&#114;&#108;&#125;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#51;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;&#38;&#32;&#61;&#32;&#123;&#51;&#125;&#94;&#123;&#52;&#45;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#53;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#125;&#32;&#38;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#51;&#45;&#50;&#125;&#125;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#125;&#123;&#57;&#125;&#32;&#38;&#61;&#32;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#50;&#53;&#125;&#38;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#49;&#125;&#125;&#32;&#92;&#92;&#32;&#32;&#57;&#38;&#32;&#61;&#32;&#57;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#38;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"207\" style=\"vertical-align: -51px;\" \/><\/p>\n<p id=\"fs-id1169596373087\">A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/>. From your earlier work with fractions, you know that:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-de877698b2f36fd6143a4e2f8db56b98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#125;&#61;&#49;&#32;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#49;&#99;&#109;&#125;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#49;&#55;&#125;&#61;&#49;&#32;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#49;&#99;&#109;&#125;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#51;&#125;&#123;&#45;&#52;&#51;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"257\" style=\"vertical-align: -12px;\" \/><\/p>\n<p id=\"fs-id1169596522381\">In words, a number divided by itself is 1. So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-665caf1b4fdeec6cc3727ea2c521ab75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#120;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"44\" style=\"vertical-align: -12px;\" \/>, for any <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fbfed3bcccaa532b43763ac59774e365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#110;&#101;&#32;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\" \/>, since any number divided by itself is 1<\/p>\n<p id=\"fs-id1169596522415\">The Quotient Property for Exponents shows us how to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2de859c9fc04f344d085c0e8fbbc1dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> by subtracting exponents. What if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88dece3773d823856db55892f4601cd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"50\" style=\"vertical-align: 0px;\" \/>?<\/p>\n<p id=\"fs-id1169596362502\">Consider <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f2ea1e2966af14aa3a36d2ac5f3fd95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>, which we know is 1<\/p>\n<table id=\"eip-158\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d34f93b1c58f0cdae08d2c4f979802d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#56;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"42\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f823039e03edb15daaff71ce826ec6de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract exponents.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f380a838e4c421a1dcd7e6dc4e408eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#45;&#51;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e5553b60802088fd831b029bc495768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596534031\">Now we will simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> in two ways to lead us to the definition of the zero exponent. In general, for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>:<\/p>\n<p><span id=\"fs-id1169596534061\" data-type=\"media\" data-alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_05_005_img_new.jpg\" alt=\"This figure is divided into two columns. At the top of the figure, the left and right columns both contain a to the m power divided by a to the m power. In the next row, the left column contains a to the m minus m power. The right column contains the fraction m factors of a divided by m factors of a, represented in the numerator and denominator by a times a followed by an ellipsis. All the as in the numerator and denominator are canceled out. In the bottom row, the left column contains a to the zero power. The right column contains 1.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596534074\">We see <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4e8d8354e6144c2fa10c26700e44e968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"23\" style=\"vertical-align: -12px;\" \/> simplifies to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8fd43f87b436f4fe4a10f792fc700a2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> and to 1. So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1169596531077\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Zero Exponent<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596531378\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a non-zero number, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1169596531400\">Any nonzero number raised to the zero power is 1<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><a id=\"example3\"><\/a>EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531411\" data-type=\"problem\">\n<p id=\"fs-id1169596531413\">Simplify:\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-177b19cd5ac49a158b35dc1012ffdf5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#45;&#57;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/> .<\/p>\n<\/div>\n<div id=\"fs-id1169596397936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596397941\">The definition says any non-zero number raised to the zero power is 1<\/p>\n<table id=\"eip-501\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Use the definition of the zero exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-90bbfc8a41df13be386e16ca051ae970_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#57;&#125;&#94;&#123;&#48;&#125;&#92;&#92;&#32;&#49;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"16\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596529728\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596529731\" data-type=\"exercise\">\n<div id=\"fs-id1169596529733\" data-type=\"problem\">\n<p id=\"fs-id1169596529735\">Simplify:\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-10d56d39f7e9eafd0b02e0986785f196_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#45;&#49;&#46;&#53;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596533793\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596533796\">\u00a01<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>Now that we have defined the zero exponent, we can expand all the Properties of Exponents to include whole number exponents.<\/p>\n<h1>Use the Definition of a Negative Exponent<\/h1>\n<p id=\"fs-id1169597357807\">\u00a0Now, let&#8217;s use the definition of a <em data-effect=\"italics\">negative exponent <\/em>to simplify expressions<em data-effect=\"italics\">.<\/em><\/p>\n<div id=\"fs-id1169597337099\" 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\">Negative Exponent<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is an integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597576960\">The <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> tells us we can re-write the expression by taking the reciprocal of the base and then changing the sign of the exponent.<\/p>\n<p id=\"fs-id1169597478894\">Any expression that has negative exponents is not considered to be in simplest form. We will use the definition of a <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> and other properties of exponents to write the expression with only positive exponents.<a id=\"example4\"><\/a><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597358215\" data-type=\"problem\">\n<p id=\"fs-id1169597383767\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7119b47c2754863932bf1d152b8ef99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-eea810a09e75c2035d30b334ec50e8ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597393699\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-426\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7119b47c2754863932bf1d152b8ef99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c13d748315f04f49d3b264566efd96e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e9355787b51ad9db1922ec074556dd6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-eea810a09e75c2035d30b334ec50e8ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-901d64f81827792caea49c0da27aa776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"21\" style=\"vertical-align: -8px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1fea2fccb14803fabd4b58d254a01be6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"28\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\n<p id=\"fs-id1169597341315\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5dfe05222e5d0c99a8f33463a9a690ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cba199993a1ce2b1fbd835dfd62f57f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597541824\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9de931d332a83dd3da0c1ba21347996c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2607673e80a6dd8bcdf0d0c4206145aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"21\" style=\"vertical-align: -8px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597339847\">In <a class=\"autogenerated-content\" href=\"#example4\">(Example 4)<\/a> we raised an integer to a negative exponent. What happens when we raise a fraction to a negative exponent? We\u2019ll start by looking at what happens to a fraction whose numerator is one and whose denominator is an integer raised to a negative exponent.<\/p>\n<table id=\"eip-532\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09928bfbc97e78137aa4bebf1cb4e265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#92;&#45;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"16\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5569bd2a061e46a91089b0d009d96c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"19\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the complex fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-448708d281429a0addf578d2518881da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597484548\">This leads to the Property of Negative Exponents.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Property of Negative Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is an integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-94b0ed444e2d2b0f50ab512a82ccce09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597577846\" data-type=\"note\">\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-id1169597529407\" data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5bf18f88bccdc8c2344001da51742a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597395509\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-453\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5bf18f88bccdc8c2344001da51742a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the property of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-94b0ed444e2d2b0f50ab512a82ccce09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f822400c3e4401570e870603d1f90afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" 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 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597467255\" data-type=\"problem\">\n<p id=\"fs-id1169597527634\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6c66d68848884d1f27cef4bef647981e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597500869\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597465620\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597393899\">Suppose now we have a fraction raised to a negative exponent. Let\u2019s use our definition of negative exponents to lead us to a new property.<\/p>\n<table id=\"eip-239\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5c56dd33660796b318e0cba381f58b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a1a75554ef6e6bab173bcc5846c19830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"31\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2e4eb06623ac7e51c5c5c8ca6a24dab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"16\" style=\"vertical-align: -14px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the complex fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cb02f0026d8b2e4046f614fa225e207e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>But we know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cb02f0026d8b2e4046f614fa225e207e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-35d39b7425f67129293e9e1d8c08b7e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>This tells us that:<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3715db0ffe0054c79bccce40b3992520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"101\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597409988\">To get from the original fraction raised to a negative exponent to the final result, we took the reciprocal of the base\u2014the fraction\u2014and changed the sign of the exponent.<\/p>\n<p id=\"fs-id1169597515519\">This leads us to the <em data-effect=\"italics\">Quotient to a Negative Power Property<\/em>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient to a Negative Exponent Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4649a8b659da898542795396b27208da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/> are real numbers, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a068d10333b909026eda652326b4441e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;&#44;&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is an integer, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2542013f8c073f8e56b93dba32f9541d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597416290\" data-type=\"note\">\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-id1169597577456\" data-type=\"problem\">\n<p id=\"fs-id1169597492476\">Simplify:\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88c423f1c5a93f40d4a2d3a4d12fa516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> .<\/p>\n<\/div>\n<div id=\"fs-id1169597580588\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-116\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 700.868px;\"><\/td>\n<td style=\"width: 228.646px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88c423f1c5a93f40d4a2d3a4d12fa516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 700.868px;\">Use the Quotient to a Negative Exponent Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2542013f8c073f8e56b93dba32f9541d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"width: 228.646px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 700.868px;\">Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\n<td style=\"width: 228.646px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c3cb35ddfb7f28fb2cdb6847d54f2b78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 700.868px;\">Simplify.<\/td>\n<td style=\"width: 228.646px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad3eef5a6b9153f5169702e6f3b6482e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597520921\" data-type=\"problem\">\n<p id=\"fs-id1169597467530\">Simplify:\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b339d4bcdf24d618b2b75c5312d07ac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> .<\/p>\n<\/div>\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597507465\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-39df5cf8ce7c780ae1d925ba712e9630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597422172\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597533646\" data-type=\"exercise\">\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\n<p>When simplifying an expression with exponents, we must be careful to correctly identify the base.<\/p>\n<\/div>\n<\/div>\n<\/div>\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-id1169597540378\" data-type=\"problem\">\n<p id=\"fs-id1169597703489\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-64fe5e608a5e73c0b94bf017509a86e6_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;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b88a360eeafca95308478b4eb3221f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e3188d9a34a0b6ceac98e9ce83ad444d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3460258d9588c748572575c810e114f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597467914\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-407\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>a) Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-64fe5e608a5e73c0b94bf017509a86e6_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;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41e94755f7b68e762d55b1e9d33f56e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"45\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6cad8eec3d159e52efa483f5f56c5d60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b) The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b88a360eeafca95308478b4eb3221f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> means &#8220;find the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df9caf63ddf8a1ffddd01a15878bf90a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/>.&#8221; Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-146e9a2e6c9eec8ce748a7bf1cd1d2b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"37\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b88a360eeafca95308478b4eb3221f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a product with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b94e847abbf5331d5e599ab80497d3a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-32a71b4cdb7c55742a7928ea7a525d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-579bbd4687145ea7c88f861b7d47e73e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c) Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-146e9a2e6c9eec8ce748a7bf1cd1d2b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"37\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e3188d9a34a0b6ceac98e9ce83ad444d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9840ffcdc626ff69bc6494a3aa4008f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d) The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3460258d9588c748572575c810e114f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/> means &#8220;find the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-451f9e5f8cc8a1b542db90c3171c815f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/>.&#8221; Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b42ce3d077a02a294b7d67ee664a56ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a product with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-25b1bc2207de590e234e54e94592a281_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-218fcba75003c7e7d9597f8c2a785e95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"68\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" 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 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597457044\" data-type=\"problem\">\n<p id=\"fs-id1169597457046\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-708748a9a14e79bf82b5aecdd49e2b88_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;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-59752c815b075c41acae607bf3714450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17503d47acc3d9d7befa5eabd5ee3a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-473ec50a16280d30e478f944d640a95c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577197\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597577199\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-987c8c247ee1bfbcaa09ef7b7ce42fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62a8b57557c69941a0a4c25e75a2b1f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/> c) 25 d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-170b493658855d7211748be1a7029d86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597533353\">We must be careful to follow the Order of Operations. In the next example, parts (a) and (b) look similar, but the results are different.<\/p>\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-id1169597492583\" data-type=\"problem\">\n<p id=\"fs-id1169597492586\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-faa0614aa2227c7e35bd54549eaf0d83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#123;&#50;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-98939c9872d5ca9e23fd3878e63c71a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597684591\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-779\" style=\"width: 100%;\" summary=\"\/\">\n<tbody>\n<tr>\n<td>a)<br \/>\nDo exponents before multiplication.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-faa0614aa2227c7e35bd54549eaf0d83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#123;&#50;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2e66df7782e402a5a6c3276fa1b2d7d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"38\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-98939c9872d5ca9e23fd3878e63c71a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-31d7f3418a7a2ed291bacf6287774849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0e150039e28dafa6054f5933f96a9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-440e70ef47f47ecc4ab7346edebafd7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#56;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9de931d332a83dd3da0c1ba21347996c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597479266\" data-type=\"problem\">\n<p id=\"fs-id1169597689696\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82794e9ba99b8e8278c5f47a83db761f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#123;&#51;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dbb5d64fd471dfcd631b8bf590531cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597576993\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597576996\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c941635aee3ad755a20c4f155a111518_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use Formulas with Exponents in Applications<\/h1>\n<p id=\"fs-id1931140\">In this section, we will use geometry formulas that contain exponents to solve problems. Since we will be solving applications, we will once again show our Problem-Solving Strategy for Geometry Applications.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Problem Solving Strategy for Geometry Applications<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"CNX_BMath_Figure_09_06_001\" class=\"bc-figure figure\">\n<div id=\"CNX_BMath_Figure_09_06_002\" class=\"bc-figure figure\">\n<p id=\"fs-id1171505481979\">A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, <em data-effect=\"italics\">s<\/em> for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe52ee4ff94040749ac3fa4744024ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#86;&#61;&#76;&#87;&#72;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#86;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#43;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#43;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#86;&#61;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"350\" style=\"vertical-align: -33px;\" \/><\/p>\n<p id=\"fs-id1767806\">So for a cube, the formulas for volume and surface area are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1560075\" 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\">Volume and Surface Area of a Cube<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1516282\">For any cube with sides of length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>,<\/p>\n<p><span id=\"fs-id1171496258265\" data-type=\"media\" data-alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_010_img.jpg\" alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\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-id1171496189268\" data-type=\"problem\">\n<p id=\"fs-id1171505620889\">A cube is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> inches on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1585408\" 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-id1784097\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168466154480\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2.5 by 2.5 by 2.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168469766852\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_040_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168465993815\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a619c720937dde578e517323cbc961de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"81\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7d276019cf15220de9d28d2000f01048_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#49;&#53;&#46;&#54;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check your work.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 15.625 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466275896\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3f584c03750ef76028c874d7fdb4646f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"101\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d70a69ededf39b23cfc9a38bf016b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#51;&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 37.5 square inches.<\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1489297\" data-type=\"problem\">\n<p id=\"fs-id1529247\">For a cube with side 4.5 metres, find the a) volume and b) surface area of the cube.<\/p>\n<\/div>\n<div id=\"fs-id1933234\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466248223\" class=\"circled\" type=\"a\">\n<li>91.125 cu. m<\/li>\n<li>121.5 sq. m<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1452349\" data-type=\"exercise\"><\/div>\n<\/div>\n<div id=\"fs-id1590812\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1418268\" data-type=\"exercise\">\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\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-id1171506138160\" data-type=\"problem\">\n<p id=\"fs-id1171505934498\">A notepad cube measures <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467296950\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2 by 2 by 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168467496838\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_041_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467188434\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0d786f11e2d8f73bb49592bae354f7b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f376b6f7054c6baa0905cae4d0c5c48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check that you did the calculations<br \/>\ncorrectly.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 8 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468478236\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bc026354a09a69cc872a4927311b0ab7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-685c7151adb58b7b872e79b47c524bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 24 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1927378\" data-type=\"problem\">\n<p id=\"fs-id1871924\">A packing box is a cube measuring <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> feet on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171511527503\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\n<li>64 cu. ft<\/li>\n<li>96 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1038661\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2058174\" data-type=\"exercise\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1954343\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\n<p id=\"eip-745\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-980f77b67737a79200c69c26bf9f365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1171512117057\" 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\">Volume and Surface Area of a Sphere<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1171512117850\">For a sphere with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f712f0944335b41e5bfeb84febf17f27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><span id=\"fs-id1171505277582\" data-type=\"media\" data-alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_015.jpg\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\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-id1171498454044\" data-type=\"problem\">\n<p id=\"fs-id1171498401975\">A sphere has a radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1650050\" 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-id1171512511594\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168468504255\" style=\"width: 100%;\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a sphere. The radius is labeled 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label<br \/>\nit with the given information.<\/td>\n<td><span id=\"eip-id1168468504279\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466046693\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c7e25a744b15835f98879ff2be16df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-47117201447fb5bbe61ff235596c3161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#54;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"116\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-232cc8d89929a2db3655c6fbcaf38d9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#57;&#48;&#52;&#46;&#51;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#117;&#98;&#105;&#99;&#32;&#105;&#110;&#99;&#104;&#101;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"184\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 904.32 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467263246\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cef1f49eebfcd3582a52a057f75f77a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7528e0026a5257ca5bf0e49a9cd354a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#54;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-af9daf4cff136e2e88f8c8356d87c20a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#53;&#50;&#46;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 452.16 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1913002\" data-type=\"problem\">\n<p id=\"fs-id1171488074403\">Find the a) volume and b) surface area of a sphere with radius 3 centimetres.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466006411\" class=\"circled\" type=\"a\">\n<li>113.04 cu. cm<\/li>\n<li>113.04 sq. cm<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171506644186\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2091579\" data-type=\"exercise\"><\/div>\n<\/div>\n<div id=\"fs-id1171498000511\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id748315\" data-type=\"solution\">\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-id945308\" data-type=\"problem\">\n<p id=\"fs-id1566505\">A globe of Earth is in the shape of a sphere with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres. Find its a) volume and b) surface area. Round the answer to the nearest hundredth.<\/p>\n<\/div>\n<div id=\"fs-id1171488252639\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467368787\" style=\"width: 100%;\" summary=\"Step 1. Read the problem.\u201d Beside this is an image of a globe. The radius is labeled 14.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw a figure with the<br \/>\ngiven information and label it.<\/td>\n<td><span id=\"eip-id1168467309173\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168464926516\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c7e25a744b15835f98879ff2be16df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e0632b43fd5e828b2088fdea44f0cd03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#49;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f331cc81c0f608896a4caf8206f56846_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#49;&#44;&#52;&#56;&#56;&#46;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 11,488.21 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468466725\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cef1f49eebfcd3582a52a057f75f77a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f262fde23f978280f04369b8ab9ff275_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#49;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f559e685ed3e244a28bc7f109d72173b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#52;&#54;&#49;&#46;&#55;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 2461.76 square inches.<\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1561201\" data-type=\"problem\">\n<p id=\"fs-id1398847\">A beach ball is in the shape of a sphere with radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1531978\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468772882\" class=\"circled\" type=\"a\">\n<li>3052.08 cu. in.<\/li>\n<li>1017.36 sq. in.<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1418575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1398911\" data-type=\"exercise\"><\/div>\n<\/div>\n<h1>Convert from Decimal Notation to Scientific Notation<\/h1>\n<p id=\"fs-id1169597689470\">Remember working with place value for whole numbers and decimals? Our number system is based on powers of 10. We use tens, hundreds, thousands, and so on. Our decimal numbers are also based on powers of tens\u2014tenths, hundredths, thousandths, and so on. Consider the numbers 4,000 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ea273f558139e4fe955e15ff72c35629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/>. We know that 4,000 means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6769a867a9c1fef29fb1c91ec0006169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/> and 0.004 means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4f60bc615d7222980709703fa032d4a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"72\" style=\"vertical-align: -9px;\" \/>.<\/p>\n<p id=\"fs-id1169597740645\">If we write the 1000 as a power of ten in exponential form, we can rewrite these numbers in this way:<\/p>\n<div id=\"fs-id1169597740648\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71b037aed4d8a1e399b0dc0b5723ba01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#52;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"274\" style=\"vertical-align: -34px;\" \/><\/div>\n<p id=\"fs-id1169597742460\">When a number is written as a product of two numbers, where the first factor is a number greater than or equal to one but less than 10, and the second factor is a power of 10 written in exponential form, it is said to be in <em data-effect=\"italics\">scientific notation.<\/em><\/p>\n<div id=\"fs-id1169597742470\" 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\">Scientific Notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597742475\">A number is expressed in scientific notation when it is of the form<\/p>\n<div id=\"fs-id1169597742489\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5d07351d30a122d374142ff84adce518_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#92;&#108;&#101;&#32;&#97;&#60;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#97;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"346\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597516025\">It is customary in scientific notation to use as the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d3e9e1d80fed18c229ee636acc0bcb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\" \/> multiplication sign, even though we avoid using this sign elsewhere in algebra.<\/p>\n<p id=\"fs-id1169597523393\">If we look at what happened to the decimal point, we can see a method to easily convert from decimal notation to <span class=\"no-emphasis\" data-type=\"term\">scientific notation<\/span>.<\/p>\n<p><span id=\"fs-id1169597523406\" data-type=\"media\" data-alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_002_img_new.jpg\" alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169597523423\">In both cases, the decimal was moved 3 places to get the first factor between 1 and 10<\/p>\n<p id=\"fs-id1169594046599\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-decd1d70a5e247a0d1fc6fc93d90b409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#112;&#111;&#119;&#101;&#114;&#32;&#111;&#102;&#32;&#49;&#48;&#32;&#105;&#115;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#32;&#119;&#104;&#101;&#110;&#32;&#116;&#104;&#101;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#32;&#105;&#115;&#32;&#108;&#97;&#114;&#103;&#101;&#114;&#32;&#116;&#104;&#97;&#110;&#32;&#49;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#52;&#44;&#48;&#48;&#48;&#61;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#112;&#111;&#119;&#101;&#114;&#32;&#111;&#102;&#32;&#49;&#48;&#32;&#105;&#115;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#119;&#104;&#101;&#110;&#32;&#116;&#104;&#101;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#32;&#105;&#115;&#32;&#98;&#101;&#116;&#119;&#101;&#101;&#110;&#32;&#48;&#32;&#97;&#110;&#100;&#32;&#49;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#48;&#46;&#48;&#48;&#52;&#61;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"696\" style=\"vertical-align: -15px;\" \/><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Convert from Decimal Notation to Scientific Notation<\/div>\n<div id=\"fs-id1169597691148\" data-type=\"exercise\">\n<div id=\"fs-id1169597691150\" data-type=\"problem\">\n<p id=\"fs-id1169597691152\">Write in scientific notation: 37,000.<\/p>\n<\/div>\n<div id=\"fs-id1169597691157\" 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><span id=\"fs-id1169597691159\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.\u201d The second cell reads \u201cRemember, there is a decimal at the end of 37,000.\u201d The third cell contains 37,000. One line down, the second cell reads \u201cMove the decimal after the 3. 3.7000 is between 1 and 10.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.\u201d The second cell reads \u201cRemember, there is a decimal at the end of 37,000.\u201d The third cell contains 37,000. One line down, the second cell reads \u201cMove the decimal after the 3. 3.7000 is between 1 and 10.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691266\" data-type=\"media\" data-alt=\"In the second row, the first cell reads \u201cStep 2. Count the number of decimal places, n, that the decimal place was moved. The second cell reads \u201cThe decimal point was moved 4 places to the left.\u201d The third cell contains 370000 again, with an arrow showing the decimal point jumping places to the left from the end of the number until it ends up between the 3 and the 7.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003b_img_new.jpg\" alt=\"In the second row, the first cell reads \u201cStep 2. Count the number of decimal places, n, that the decimal place was moved. The second cell reads \u201cThe decimal point was moved 4 places to the left.\u201d The third cell contains 370000 again, with an arrow showing the decimal point jumping places to the left from the end of the number until it ends up between the 3 and the 7.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691281\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Write the number as a product with a power of 10. If the original number is greater than 1, the power of 10 will be 10 to the n power. If it\u2019s between 0 and 1, the power of 10 will be 10 to the negative n power.\u201d The second cell reads \u201c37,000 is greater than 1, so the power of 10 will have exponent 4.\u201d The third cell contains 3.7 times 10 to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Write the number as a product with a power of 10. If the original number is greater than 1, the power of 10 will be 10 to the n power. If it\u2019s between 0 and 1, the power of 10 will be 10 to the negative n power.\u201d The second cell reads \u201c37,000 is greater than 1, so the power of 10 will have exponent 4.\u201d The third cell contains 3.7 times 10 to the fourth power.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597691296\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Check.\u201d The second cell reads \u201cCheck to see if your answer makes sense.\u201d The third cell reads \u201c10 to the fourth power is 10,000 and 10,000 times 3.7 will be 37,000.\u201d Below this is 37,000 equals 3.7 times 10 to the fourth power.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_003d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Check.\u201d The second cell reads \u201cCheck to see if your answer makes sense.\u201d The third cell reads \u201c10 to the fourth power is 10,000 and 10,000 times 3.7 will be 37,000.\u201d Below this is 37,000 equals 3.7 times 10 to the fourth power.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536011\" data-type=\"problem\">\n<p id=\"fs-id1169597536013\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9aed06fb54414c85278a4ce7caafd8c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#54;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597536022\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597536024\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-99cf324da7d785d905df59f3ced114ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Convert from decimal notation to scientific notation<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1168743403951\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\n<li>Count the number of decimal places, <em data-effect=\"italics\">n<\/em>, that the decimal point was moved.<\/li>\n<li>Write the number as a product with a power of 10.<br \/>\nIf the original number is:<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<ul id=\"fs-id1168744092452\" data-bullet-style=\"bullet\">\n<li>greater than 1, the power of 10 will be 10<sup><em data-effect=\"italics\">n<\/em><\/sup>.<\/li>\n<li>between 0 and 1, the power of 10 will be 10<sup><em data-effect=\"italics\">\u2212n<\/em><\/sup>.<\/li>\n<li>Check.<\/li>\n<\/ul>\n<div id=\"fs-id1168743403943\" class=\"howto\" data-type=\"note\">\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-id1169597701094\" data-type=\"problem\">\n<p id=\"fs-id1169597701096\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0919240c93f24e7c0d4a1db444cb2954_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597701105\" 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-id1169597701107\">The original number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0919240c93f24e7c0d4a1db444cb2954_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/>, is between 0 and 1 so we will have a negative power of 10<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 115px;\">\n<tbody>\n<tr style=\"height: 25px;\">\n<td style=\"width: 50%; height: 25px;\"><\/td>\n<td style=\"width: 50%; height: 25px;\"><span id=\"eip-id1172181050459\" data-type=\"media\" data-alt=\"0.0052.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004a_img_new.jpg\" alt=\"0.0052.\" width=\"110\" height=\"11\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Move the decimal point to get 5.2, a number between 1 and 10.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050475\" data-type=\"media\" data-alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004b_img_new.jpg\" alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\" width=\"119\" height=\"17\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Count the number of decimal places the point was moved.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050492\" data-type=\"media\" data-alt=\"3 places.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004c_img_new.jpg\" alt=\"3 places.\" width=\"118\" height=\"16\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Write as a product with a power of 10.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1172181050509\" data-type=\"media\" data-alt=\"5.2 times 10 to the power of negative 3.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_004d_img_new.jpg\" alt=\"5.2 times 10 to the power of negative 3.\" width=\"123\" height=\"12\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Check.<\/td>\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6112f497e041c002f6b15cd3e7ef669f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"92\" style=\"vertical-align: -55px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a1c13e64ff50b85e1e1afc476c761229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\"><\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597577078\" data-type=\"problem\">\n<p id=\"fs-id1169597577080\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7db51e7c60feebbd078e83e6a79849c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#55;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577089\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597577091\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71c90db96f02a2ada5561b41ec486fb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Convert Scientific Notation to Decimal Form<\/h1>\n<p id=\"fs-id1169597555698\">How can we convert from scientific notation to decimal form? Let\u2019s look at two numbers written in scientific notation and see.<\/p>\n<div id=\"fs-id1169597555702\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c5e8dc7a6d38c770355a60127e55121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#48;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#49;&#44;&#50;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#48;&#57;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"341\" style=\"vertical-align: -26px;\" \/><\/div>\n<p id=\"fs-id1169597688301\">If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.<\/p>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9026adb95813e623494ae08b74bb6c70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#61;&#57;&#49;&#44;&#50;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#61;&#48;&#46;&#48;&#48;&#48;&#57;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"468\" style=\"vertical-align: -4px;\" \/><\/div>\n<p><span id=\"fs-id1169597742376\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_02_015_img.jpg\" alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169597742371\">In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.<\/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 data-type=\"title\">How to Convert Scientific Notation to Decimal Form<\/div>\n<div id=\"fs-id1169597741743\" data-type=\"exercise\">\n<div id=\"fs-id1169597741745\" data-type=\"problem\">\n<p id=\"fs-id1169597741747\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-657431bc9e19b8ebb48da9f98f060126_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597741764\" 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><span id=\"fs-id1169597741774\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006a_img_new.jpg\" alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597741789\" data-type=\"media\" data-alt=\"In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006b_img_new.jpg\" alt=\"In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169597741802\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_006c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597741410\" data-type=\"problem\">\n<p id=\"fs-id1169597741412\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1f1e78032d1e5e4db8dccfa83d1297d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597741429\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597741431\">1,300<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597505408\">The steps are summarized below.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Convert scientific notation to decimal form.<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597505421\">To convert scientific notation to decimal form:<\/p>\n<ol id=\"fs-id1168746296183\" class=\"stepwise\" type=\"1\">\n<li>Determine the exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, on the factor 10.<\/li>\n<li>Move the decimal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> places, adding zeros if needed.\n<ul id=\"fs-id1169597505448\" data-bullet-style=\"bullet\">\n<li>If the exponent is positive, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> places to the right.<\/li>\n<li>If the exponent is negative, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b38a586dc76a31dfa818cbaca2da26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\" \/> places to the left.<\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597505412\" class=\"howto\" data-type=\"note\">\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-id1169597744324\" data-type=\"problem\">\n<p id=\"fs-id1169597744326\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-515fcac8c7cee1af1941d525a061414f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597744344\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187383117\" style=\"width: 100%;\" summary=\"This figure has two columns. At the top of the figure, in the right column is 8.9 times 10 to the negative second power. One row down, the text in the left column says \u201cDetermine the exponent, n, on the factor 10.\u201d The right column says \u201cThe exponent is negative 2.\u201d One row down, the text in the left column says \u201cSince the exponent is negative, move the decimal point 2 places to the left.\u201d The right column contains 8.9, with an arrow showing the decimal point in 9.12 being moved two places to the left. Because there are no digits before 8, the remaining places are represented by spaces. One row down, the text in the left says \u201cAdd zeros as needed for placeholders.\u201d The right column contains 8.9 times 10 to the negative second power equals 0.089.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187383136\" data-type=\"media\" data-alt=\"8.9 times 10 to the power of negative 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007a_img_new.jpg\" alt=\"8.9 times 10 to the power of negative 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Determine the exponent, <em data-effect=\"italics\">n<\/em>, on the factor 10.<\/td>\n<td><span id=\"eip-id1172187383152\" data-type=\"media\" data-alt=\"The exponent is negative 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007b_img_new.jpg\" alt=\"The exponent is negative 2.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Since the exponent is negative, move the decimal point 2 places to the left.<\/td>\n<td><span id=\"eip-id1172187383169\" data-type=\"media\" data-alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007c_img_new.jpg\" alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add zeros as needed for placeholders.<\/td>\n<td><span id=\"eip-id1172187383201\" data-type=\"media\" data-alt=\"8.9 times 10 to the power of negative 2 equals 0.089.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_06_07_007e_img_new.jpg\" alt=\"8.9 times 10 to the power of negative 2 equals 0.089.\" 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 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597739737\" data-type=\"problem\">\n<p id=\"fs-id1169597739739\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1227f836a6bd3017d439530d34d7b8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597739758\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597739760\">0.00012<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Multiply and Divide Using Scientific Notation<\/h1>\n<p id=\"fs-id1169597704318\">Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\n<p id=\"fs-id1169597704332\">Multiply. Write answers in decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4c09d3c3460859f9a212a0daf66df621_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-13cd37397b57a13c851723b8f27e6b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Use the Commutative Property to rearrange the factors.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-15198a527406018dfdae5329e6847e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Multiply.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-37020fcd09f2af127506e6ca4bebe6b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Change to decimal form by moving the decimal two places left.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7f8719a7641b612218fb59fb49afe49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576869\" data-type=\"problem\">\n<p id=\"fs-id1169597576871\">Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-30b7ec6edfae88819ab6f3e8c96e3477_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597533139\">0.06<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597576863\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597576867\" data-type=\"exercise\">\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\n<p id=\"fs-id1169597704332\">Multiply. Write answer in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-84a114fe887007d34e64029a7a69213d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"196\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a0add93fd04f7ba74e1b9bdd077f52f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#46;&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"182\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Use the Commutative Property to rearrange the factors.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b7200804fbfc337fbb806acf2a06fbc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#46;&#51;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"145\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Multiply.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e01d13634af5727a6b4360013a7eb41d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#46;&#49;&#54;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Write the answer in scientific notation.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ca12e7188bb3cc5db95d0ce796feb280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#48;&#49;&#54;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\n<p id=\"fs-id1169597539395\">Multiply. Write answer in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-48bc450dab5c6e6d8c90fbd1808e71a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#46;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"196\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597539428\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-174323e1e5c281c4a034f0eb1303de73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#49;&#51;&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"98\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\n<p id=\"fs-id1169597705347\">Divide. Write answers in decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cd816f9f56010de8ae65379ca19f48af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-472a1306a7393eb6c3eff6c66dc3a193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Separate the factors, rewriting as the product of two fractions.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-70d16e22fba2f1c1c40668898aab4e18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide.<\/td>\n<td style=\"width: 50%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5deba0e00f6c34d127c5d6a4fecc1b3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Change to decimal form by moving the decimal five places right.<\/td>\n<td style=\"width: 50%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-59d018ab7ed311e82b5003dade558a63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#48;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\n<p id=\"fs-id1169597539395\">Divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00d6a7247b1f3967d95dff09564a92a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597539428\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597539431\">400,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597533145\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597533149\" data-type=\"exercise\">\n<div id=\"fs-id1169597705332\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\n<p id=\"fs-id1169597705347\">Divide. Write answer in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2d84a242fb0e46e585ff8418254b5ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"56\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2129d89b3d8dfc23570ed5aa830f57d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#46;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#56;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"49\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Separate the factors, rewriting as the product of two fractions.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-abdbcbcf18226383b9e2775734aa3797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#46;&#50;&#125;&#123;&#56;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"73\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide.<\/td>\n<td style=\"width: 50%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b59e164cfe0cb06e3fbfa3fc2c7d1325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Write answer in scientific notation<\/td>\n<td style=\"width: 50%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-14416ed3ca890a8973ab03884e4c8ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\n<p id=\"fs-id1169597539395\">Divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-242c864c967d3509cfd93f9c5e743828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#46;&#53;&#56;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#51;&#46;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"70\" style=\"vertical-align: -7px;\" \/>. Write answer in scientific notation.<\/p>\n<\/div>\n<div id=\"fs-id1169597539428\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597539431\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-adc1812ed8d9d88aa99a2d441820c813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Access these online resources for additional instruction and practice with integer exponents and scientific notation:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597739988\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id1169597739997\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25Negexponents\">Negative Exponents<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot1\">Scientific Notation<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot2\">Scientific Notation 2<\/a><\/li>\n<\/ul>\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\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/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\">Product Property 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\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-100f4fb1ff0dc07a5251b86808eb0f79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul id=\"fs-id1169597689120\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Quotient Property for Exponents:<\/strong>\n<ul id=\"fs-id1169596530872\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a real number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d388c5467ca8f0ee93f59d2cca11eaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"112\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0396edebe223a835ea4e9b14f4271745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#97;&#110;&#100;&#32;&#125;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#125;&#44;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"165\" style=\"vertical-align: -12px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Zero Exponent<\/strong>\n<ul id=\"fs-id1169596398934\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a non-zero number, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1001cb2e5ed58ec551bbd3d4da4e0b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Property of Negative Exponents<\/strong>\n<ul id=\"fs-id1169597689133\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is a positive integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df2afd8a9cb6add6da009531338a6949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-94b0ed444e2d2b0f50ab512a82ccce09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Quotient to a Negative Exponent<\/strong>\n<ul id=\"fs-id1169597689185\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is an integer , then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2542013f8c073f8e56b93dba32f9541d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">To convert a decimal to scientific notation:<\/strong>\n<ol id=\"fs-id1168746309069\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\n<li>Count the number of decimal places, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, that the decimal point was moved.<\/li>\n<li>Write the number as a product with a power of 10. If the original number is:\n<ul id=\"fs-id1169596704515\" data-bullet-style=\"open-circle\">\n<li>greater than 1, the power of 10 will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2b691112cdf78d707f555818caf55d29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>between 0 and 1, the power of 10 will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0552299a1957e00bb33338572b5b8287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">To convert scientific notation to decimal form:<\/strong>\n<ol id=\"fs-id1168744116887\" class=\"stepwise\" type=\"1\">\n<li>Determine the exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, on the factor 10.<\/li>\n<li>Move the decimal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>places, adding zeros if needed.\n<ul id=\"fs-id1169597742509\" data-bullet-style=\"open-circle\">\n<li>If the exponent is positive, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> places to the right.<\/li>\n<li>If the exponent is negative, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b38a586dc76a31dfa818cbaca2da26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\" \/> places to the left.<\/li>\n<\/ul>\n<\/li>\n<li>Check<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>1.5 Exercise Set<\/h1>\n<p id=\"fs-id1168745177173\">In the following exercises, simplify each expression with exponents.<\/p>\n<ol class=\"twocolumn\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>In the following exercises, simplify.<\/p>\n<ol class=\"twocolumn\" start=\"6\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-29235d394f359e05cc3e1232453451d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#48;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-484605cd68aa07e7715ff451823e25ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-059e4762a5f2f2c710ea90514902299a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-70b2d4de96035c8614e6bdb7f70ba812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#50;&#55;&#125;&#94;&#123;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>In the following exercises, simplify.<\/p>\n<ol class=\"twocolumn\" start=\"8\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d1e394764b0c897179716899b636ed4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a2adce90e7fd78901b14540423deb0c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e60cc72d4ea2160c7c3befeba2dbbe0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e110ce51a036e0f09a691128e9f9525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#40;&#45;&#49;&#48;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d3c6f11c1522a9b5d8c22c4de9ca78e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e6f625c8038bff780e2a409fc14b2367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"30\" style=\"vertical-align: -8px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1fd82971a75b184e7d77fd65722fca8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-15846b19e458df15df217cd18be692ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-86af125d788a96b72e00c5fbd8450589_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e55e2dd566609e1af1caf81893107a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#55;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3dcb755458ae69c353459fa636ba6b6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ff58e06294532f91876b1ec49d74d5e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7d77bc5494e8a86d5ef5b8bd77a60f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-feb7ffb920091f80e599eb6997adb506_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9df28c1bca24e427c5c74303f6139e74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-178e1a9611887eb63e1a913fd1d4ce52_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;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-503911ff42198edc9a66a5272a76a58a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#123;&#53;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-18add71bd9cc7cdabffab90a3a58730b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3007c9216bbd65210f657f34ea830ee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-61f7364d37431b97cf43f95994966872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>In the following exercises, find a) the volume and b) the surface area of the cube with the given side length.<\/p>\n<ol class=\"twocolumn\" start=\"18\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> centimetres<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-110ffb20e30a4c62dda047c98653a72c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> feet<\/li>\n<\/ol>\n<p>In the following exercises, solve.<\/p>\n<ol start=\"20\">\n<li><strong data-effect=\"bold\">Museum<\/strong> A cube-shaped museum has sides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> metres long. Find its a) volume and b) surface area.<\/li>\n<li><strong data-effect=\"bold\">Base of statue<\/strong> The base of a statue is a cube with sides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec778b275453b1720f4962450010c189_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> metres long. Find its a) volume and b) surface area.<\/li>\n<\/ol>\n<p>In the following exercises, find a) the volume and b) the surface area of the sphere with the given radius. Round answers to the nearest hundredth.<\/p>\n<ol class=\"twocolumn\" start=\"22\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0f1744ffd0a5d1d7e31cd59aefe01c6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet<\/li>\n<\/ol>\n<p>In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n<ol start=\"24\">\n<li><strong data-effect=\"bold\">Exercise ball<\/strong> An exercise ball has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> inches. Find its a) volume and b) surface area.<\/li>\n<li><strong data-effect=\"bold\">Golf ball<\/strong> A golf ball has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8fac357af10206befdb463e651007c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -1px;\" \/> centimetres. Find its a) volume and b) surface area.<\/li>\n<\/ol>\n<p>In the following exercises, write each number in scientific notation.<\/p>\n<ol class=\"twocolumn\" start=\"26\">\n<li>340,000<\/li>\n<li>1,290,000<\/li>\n<li>0.041<\/li>\n<li>0.00000103<\/li>\n<\/ol>\n<p>In the following exercises, convert each number to decimal form.<\/p>\n<ol class=\"twocolumn\" start=\"30\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a9bf58d27ddf979d6a1b67de5cd5ecc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ed742d2711bd14e8c441052885a47ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-719b8ec246df0a5c97e396b17c40c8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e3675c6768f5533452e91527d467ef8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#57;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<p>In the following exercises, multiply. Write your answer in decimal form.<\/p>\n<ol class=\"twocolumn\" start=\"34\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5d5216a52772eef684753e67c13744d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4b9ac094377e5783d6da2a16e2155a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"206\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<p>In the following exercises, divide. Write your answer in decimal form.<\/p>\n<ol start=\"36\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0df35b3ace7f0a2686f41a8f22a3e746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;&#123;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"61\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1d3437ec8ba0d84eb1016fc89a4a1fe5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/li>\n<li>The population of the world on July 1, 2010 was more than 6,850,000,000. Write the number in scientific notation<\/li>\n<li>The probability of winning the lottery was about 0.0000000057. Write the number in scientific notation.<\/li>\n<li>The width of a proton is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ccba51e1dfa595a218fcd8213582fff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: 0px;\" \/> of the width of an atom. Convert this number to decimal form.<\/li>\n<li><strong data-effect=\"bold\">Coin production<\/strong> In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.<\/li>\n<li><strong>Debt<\/strong> At the end of fiscal year 2019 the gross Canadian federal government debt was estimated to be approximately &#36;685,450,000,000 (&#36;685.45 billion), according to the Federal Budget. The population of Canada was approximately 37,590,000 people at the end of fiscal year 2019.\n<ol type=\"a\">\n<li>Write the debt in scientific notation.<\/li>\n<li>Write the population in scientific notation.<\/li>\n<li>Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1>Answers:<\/h1>\n<ol class=\"twocolumn\">\n<li>\n<ol type=\"a\">\n<li>243<\/li>\n<li>9<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6cad8eec3d159e52efa483f5f56c5d60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>0.0016<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>64<\/li>\n<li>14<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-805ed3f3b8d88c81c79ea3ee5c7c4072_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/li>\n<li>0.49<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>1296<\/li>\n<li>\u22121296<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d1ed596631867bfaf25f7f4ead1e7c84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03691bec54827131718c68dfdca523bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>\u22120.25<\/li>\n<li>0.25<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>1<\/li>\n<li>1<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>1<\/li>\n<li>\u22121<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-413b53329a059cb8cfa09f6099b90f20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82c692fc7c77d012d64039079d9df525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-be7095bece419e2f69b75329b6a2dede_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82c692fc7c77d012d64039079d9df525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>25<\/li>\n<li>10000<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4363adf3e46b27a53bd639d7914d486a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6ae83c977dbd39163b18e6bc242d3584_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#52;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e0f5b406842eec4fd97aa861ff082dec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-98d0e28a383f2b9a740526a327d1da88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>49<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-87b45b657a37f37cb779527d2a666770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1de96f31c6c2bbd001766ad4d0631ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"36\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f7b496891eb276b3992ed20de9750b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f7b496891eb276b3992ed20de9750b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1de96f31c6c2bbd001766ad4d0631ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"36\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0700364398eac9320f4d6eebefa6d6b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a9948ce98461082e7c8558675198f9ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c2cc5f6cc44ddc16d1b1c4f3a0511b75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-49c01acf37cd400837f17c6f5449441f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#52;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>125 cu. cm<\/li>\n<li>150 sq. cm<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>1124.864 cu. ft.<\/li>\n<li>648.96 sq. ft<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>262,144 cu. ft<\/li>\n<li>24,576 sq. ft<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>21.952 cu. m<\/li>\n<li>47.04 sq. m<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>113.04 cu. cm<\/li>\n<li>113.04 sq. cm<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>1,766.25 cu. ft<\/li>\n<li>706.5 sq. ft<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>14,130 cu. in.<\/li>\n<li>2,826 sq. in.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>381.51 cu. cm<\/li>\n<li>254.34 sq. cm<\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc6d93ca28f76e08f55140137a9c2899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c22e3392801a816c7d6da104dd66c2cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3088bcce6e96dc6e3552792ff1522522_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a852a24e52e974ea50fbf68021a98c33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#48;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>830<\/li>\n<li>16,000,000,000<\/li>\n<li>0.038<\/li>\n<li>0.0000193<\/li>\n<li>0.02<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-600f03bf11b7e20a1697b4da8c75bef2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>500,000,000<\/li>\n<li>20,000,000<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4441e560a14f3a0e7760e7b0b646169e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-12c1b226d4e3fda114d8bb84d465a832_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"94\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>0.00001<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-26d39ca2978eb1b85642104f3338a5c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;&#52;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"93\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa140131fdbc8a6f2ca49ff284527b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#53;&#52;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"109\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-461f9a4a1afca53121c015ed7f1e51c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#55;&#53;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"94\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-775650bf8dd1858c34cb64b9653307f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#56;&#50;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"93\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cInteger Exponents and Scientific Notation\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":125,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-205","chapter","type-chapter","status-publish","hentry"],"part":21,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":8,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/205\/revisions"}],"predecessor-version":[{"id":2186,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/205\/revisions\/2186"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/21"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/205\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=205"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=205"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=205"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}