{"id":795,"date":"2016-06-01T20:49:09","date_gmt":"2016-06-01T20:49:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=795"},"modified":"2019-07-24T21:13:09","modified_gmt":"2019-07-24T21:13:09","slug":"read-multiply-and-divide-numbers-in-scientific-notation-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/read-multiply-and-divide-numbers-in-scientific-notation-2\/","title":{"raw":"Multiply and Divide Numbers in Scientific Notation","rendered":"Multiply and Divide Numbers in Scientific Notation"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcome<\/h3>\r\n<ul>\r\n \t<li>Multiply and divide numbers expressed in\u00a0scientific notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Multiplying and Dividing Numbers Expressed in Scientific Notation<\/h2>\r\nNumbers that are written in scientific notation can be multiplied and divided rather simply by taking advantage of the properties of numbers and the rules of exponents that you may recall. To multiply numbers in scientific notation, first multiply the numbers that are not powers of\u00a0[latex]10[\/latex] (the <i>a<\/i> in [latex]a\\times10^{n}[\/latex]). Then multiply the powers of ten by adding the exponents.\r\n\r\nThis will produce a new number times a different power of\u00a0[latex]10[\/latex]. All you have to do is check to make sure this new value is in scientific notation. If it is not, you convert it.\r\n\r\nLet us look at some examples.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\n<p style=\"text-align: center;\">Multiply [latex]\\left(3\\times10^{8}\\right)\\left(6.8\\times10^{-13}\\right)[\/latex]<\/p>\r\n[reveal-answer q=\"395606\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"395606\"]\r\n\r\nRegroup using the commutative and associative properties.\r\n<p style=\"text-align: center;\">[latex]\\left(3\\times6.8\\right)\\left(10^{8}\\times10^{-13}\\right)[\/latex]<\/p>\r\nMultiply the coefficients.\r\n<p style=\"text-align: center;\">[latex]\\left(20.4\\right)\\left(10^{8}\\times10^{-13}\\right)[\/latex]<\/p>\r\nMultiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.\r\n<p style=\"text-align: center;\">[latex]20.4\\times10^{-5}[\/latex]<\/p>\r\nConvert\u00a0[latex]20.4[\/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\left(2.04\\times10^{1}\\right)\\times10^{-5}[\/latex]<\/p>\r\nGroup the powers of\u00a0[latex]10[\/latex] using the associative property of multiplication.\r\n<p style=\"text-align: center;\">[latex]2.04\\times\\left(10^{1}\\times10^{-5}\\right)[\/latex]<\/p>\r\nMultiply using the Product Rule, so add the exponents.\r\n<p style=\"text-align: center;\">[latex]2.04\\times10^{1+\\left(-5\\right)}[\/latex]<\/p>\r\nThe answer is [latex]2.04\\times10^{-4}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\n<p style=\"text-align: center;\">Multiply [latex]\\left(8.2\\times10^{6}\\right)\\left(1.5\\times10^{-3}\\right)\\left(1.9\\times10^{-7}\\right)[\/latex]<\/p>\r\n[reveal-answer q=\"23947\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"23947\"]\r\n\r\nRegroup using the commutative and associative properties.\r\n<p style=\"text-align: center;\">[latex]\\left(8.2\\times1.5\\times1.9\\right)\\left(10^{6}\\times10^{-3}\\times10^{-7}\\right)[\/latex]<\/p>\r\nMultiply the numbers.\r\n<p style=\"text-align: center;\">[latex]\\left(23.37\\right)\\left(10^{6}\\times10^{-3}\\times10^{-7}\\right)[\/latex]<\/p>\r\nMultiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.\r\n<p style=\"text-align: center;\">[latex]23.37\\times10^{-4}[\/latex]<\/p>\r\nConvert\u00a0[latex]23.37[\/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\left(2.337\\times10^{1}\\right)\\times10^{-4}[\/latex]<\/p>\r\nGroup the powers of\u00a0[latex]10[\/latex] using the associative property of multiplication.\r\n<p style=\"text-align: center;\">[latex]2.337\\times\\left(10^{1}\\times10^{-4}\\right)[\/latex]<\/p>\r\nMultiply using the Product Rule, so add the exponents.\r\n<p style=\"text-align: center;\">[latex]2.337\\times10^{1+\\left(-4\\right)}[\/latex]<\/p>\r\nThe answer is [latex]2.337\\times10^{-3}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, you will see an example of how to multiply two numbers that are written in scientific notation.\r\n\r\nhttps:\/\/youtu.be\/5ZAY4OCkp7U\r\n\r\nIn order to divide numbers in scientific notation, you once again apply the properties of numbers and the rules of exponents. You begin by dividing the numbers that are not powers of\u00a0[latex]10[\/latex] (the <i>a<\/i> in [latex]a\\times10^{n}[\/latex]. Then you divide the powers of ten by subtracting the exponents.\r\n\r\nThis will produce a new number times a different power of [latex]10[\/latex]. If it is not already in scientific notation, you convert it, and then you are done.\r\n\r\nLet us look at some examples.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\n<p style=\"text-align: center;\">Divide [latex] \\displaystyle \\frac{2.829\\times 1{{0}^{-9}}}{3.45\\times 1{{0}^{-3}}}[\/latex]<\/p>\r\n[reveal-answer q=\"364796\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"364796\"]\r\n\r\nRegroup using the associative property.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\left( \\frac{2.829}{3.45} \\right)\\left( \\frac{{{10}^{-9}}}{{{10}^{-3}}} \\right)[\/latex]<\/p>\r\nDivide the coefficients.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\left(0.82\\right)\\left( \\frac{{{10}^{-9}}}{{{10}^{-3}}} \\right)[\/latex]<\/p>\r\nDivide the powers of\u00a0[latex]10[\/latex] using the Quotient Rule, so subtract the exponents.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}0.82\\times10^{-9-\\left(-3\\right)}\\\\0.82\\times10^{-6}\\end{array}[\/latex]<\/p>\r\nConvert\u00a0[latex]0.82[\/latex] into scientific notation by moving the decimal point one place to the right and multiplying by [latex]10^{-1}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\left(8.2\\times10^{-1}\\right)\\times10^{-6}[\/latex]<\/p>\r\nGroup the powers of 10 together using the associative property.\r\n<p style=\"text-align: center;\">[latex]8.2\\times\\left(10^{-1}\\times10^{-6}\\right)[\/latex]<\/p>\r\nMultiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.\r\n<p style=\"text-align: center;\">[latex]8.2\\times10^{-1+\\left(-6\\right)}[\/latex]<\/p>\r\nThe answer is [latex]8.2\\times {{10}^{-7}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\n<p style=\"text-align: center;\">Calculate [latex]\\displaystyle \\frac{\\left(1.37\\times10^{4}\\right)\\left(9.85\\times10^{6}\\right)}{5.0\\times10^{12}}[\/latex]<\/p>\r\n[reveal-answer q=\"337143\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"337143\"]Regroup the terms in the numerator according to the associative and commutative properties.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{\\left( 1.37\\times 9.85 \\right)\\left( {{10}^{6}}\\times {{10}^{4}} \\right)}{5.0\\times {{10}^{12}}}[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{13.4945\\times {{10}^{10}}}{5.0\\times {{10}^{12}}}[\/latex]<\/p>\r\nRegroup using the associative property.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\left( \\frac{13.4945}{5.0} \\right)\\left( \\frac{{{10}^{10}}}{{{10}^{12}}} \\right)[\/latex]<\/p>\r\nDivide the numbers.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\left(2.6989\\right)\\left(\\frac{10^{10}}{10^{12}}\\right)[\/latex]<\/p>\r\nDivide the powers of\u00a0[latex]10[\/latex] using the Quotient Rule, so subtract the exponents.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{c}\\left(2.6989 \\right)\\left( {{10}^{10-12}} \\right)\\\\2.6989\\times {{10}^{-2}}\\end{array}[\/latex]<\/p>\r\nThe answer is [latex]2.6989\\times {{10}^{-2}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that when you divide exponential terms, you subtract the exponent in the denominator from the exponent in the numerator. You will see another example of dividing numbers written in scientific notation in the following video.\r\n\r\nhttps:\/\/youtu.be\/8BX0oKUMIjw","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcome<\/h3>\n<ul>\n<li>Multiply and divide numbers expressed in\u00a0scientific notation<\/li>\n<\/ul>\n<\/div>\n<h2>Multiplying and Dividing Numbers Expressed in Scientific Notation<\/h2>\n<p>Numbers that are written in scientific notation can be multiplied and divided rather simply by taking advantage of the properties of numbers and the rules of exponents that you may recall. To multiply numbers in scientific notation, first multiply the numbers that are not powers of\u00a0[latex]10[\/latex] (the <i>a<\/i> in [latex]a\\times10^{n}[\/latex]). Then multiply the powers of ten by adding the exponents.<\/p>\n<p>This will produce a new number times a different power of\u00a0[latex]10[\/latex]. All you have to do is check to make sure this new value is in scientific notation. If it is not, you convert it.<\/p>\n<p>Let us look at some examples.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p style=\"text-align: center;\">Multiply [latex]\\left(3\\times10^{8}\\right)\\left(6.8\\times10^{-13}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q395606\">Show Solution<\/span><\/p>\n<div id=\"q395606\" class=\"hidden-answer\" style=\"display: none\">\n<p>Regroup using the commutative and associative properties.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(3\\times6.8\\right)\\left(10^{8}\\times10^{-13}\\right)[\/latex]<\/p>\n<p>Multiply the coefficients.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(20.4\\right)\\left(10^{8}\\times10^{-13}\\right)[\/latex]<\/p>\n<p>Multiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]20.4\\times10^{-5}[\/latex]<\/p>\n<p>Convert\u00a0[latex]20.4[\/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\left(2.04\\times10^{1}\\right)\\times10^{-5}[\/latex]<\/p>\n<p>Group the powers of\u00a0[latex]10[\/latex] using the associative property of multiplication.<\/p>\n<p style=\"text-align: center;\">[latex]2.04\\times\\left(10^{1}\\times10^{-5}\\right)[\/latex]<\/p>\n<p>Multiply using the Product Rule, so add the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]2.04\\times10^{1+\\left(-5\\right)}[\/latex]<\/p>\n<p>The answer is [latex]2.04\\times10^{-4}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p style=\"text-align: center;\">Multiply [latex]\\left(8.2\\times10^{6}\\right)\\left(1.5\\times10^{-3}\\right)\\left(1.9\\times10^{-7}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q23947\">Show Solution<\/span><\/p>\n<div id=\"q23947\" class=\"hidden-answer\" style=\"display: none\">\n<p>Regroup using the commutative and associative properties.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(8.2\\times1.5\\times1.9\\right)\\left(10^{6}\\times10^{-3}\\times10^{-7}\\right)[\/latex]<\/p>\n<p>Multiply the numbers.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(23.37\\right)\\left(10^{6}\\times10^{-3}\\times10^{-7}\\right)[\/latex]<\/p>\n<p>Multiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]23.37\\times10^{-4}[\/latex]<\/p>\n<p>Convert\u00a0[latex]23.37[\/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\left(2.337\\times10^{1}\\right)\\times10^{-4}[\/latex]<\/p>\n<p>Group the powers of\u00a0[latex]10[\/latex] using the associative property of multiplication.<\/p>\n<p style=\"text-align: center;\">[latex]2.337\\times\\left(10^{1}\\times10^{-4}\\right)[\/latex]<\/p>\n<p>Multiply using the Product Rule, so add the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]2.337\\times10^{1+\\left(-4\\right)}[\/latex]<\/p>\n<p>The answer is [latex]2.337\\times10^{-3}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, you will see an example of how to multiply two numbers that are written in scientific notation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples:  Multiplying Numbers Written in Scientific Notation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/5ZAY4OCkp7U?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In order to divide numbers in scientific notation, you once again apply the properties of numbers and the rules of exponents. You begin by dividing the numbers that are not powers of\u00a0[latex]10[\/latex] (the <i>a<\/i> in [latex]a\\times10^{n}[\/latex]. Then you divide the powers of ten by subtracting the exponents.<\/p>\n<p>This will produce a new number times a different power of [latex]10[\/latex]. If it is not already in scientific notation, you convert it, and then you are done.<\/p>\n<p>Let us look at some examples.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p style=\"text-align: center;\">Divide [latex]\\displaystyle \\frac{2.829\\times 1{{0}^{-9}}}{3.45\\times 1{{0}^{-3}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q364796\">Show Solution<\/span><\/p>\n<div id=\"q364796\" class=\"hidden-answer\" style=\"display: none\">\n<p>Regroup using the associative property.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\left( \\frac{2.829}{3.45} \\right)\\left( \\frac{{{10}^{-9}}}{{{10}^{-3}}} \\right)[\/latex]<\/p>\n<p>Divide the coefficients.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\left(0.82\\right)\\left( \\frac{{{10}^{-9}}}{{{10}^{-3}}} \\right)[\/latex]<\/p>\n<p>Divide the powers of\u00a0[latex]10[\/latex] using the Quotient Rule, so subtract the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}0.82\\times10^{-9-\\left(-3\\right)}\\\\0.82\\times10^{-6}\\end{array}[\/latex]<\/p>\n<p>Convert\u00a0[latex]0.82[\/latex] into scientific notation by moving the decimal point one place to the right and multiplying by [latex]10^{-1}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\left(8.2\\times10^{-1}\\right)\\times10^{-6}[\/latex]<\/p>\n<p>Group the powers of 10 together using the associative property.<\/p>\n<p style=\"text-align: center;\">[latex]8.2\\times\\left(10^{-1}\\times10^{-6}\\right)[\/latex]<\/p>\n<p>Multiply the powers of\u00a0[latex]10[\/latex] using the Product Rule, so add the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]8.2\\times10^{-1+\\left(-6\\right)}[\/latex]<\/p>\n<p>The answer is [latex]8.2\\times {{10}^{-7}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p style=\"text-align: center;\">Calculate [latex]\\displaystyle \\frac{\\left(1.37\\times10^{4}\\right)\\left(9.85\\times10^{6}\\right)}{5.0\\times10^{12}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q337143\">Show Solution<\/span><\/p>\n<div id=\"q337143\" class=\"hidden-answer\" style=\"display: none\">Regroup the terms in the numerator according to the associative and commutative properties.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\left( 1.37\\times 9.85 \\right)\\left( {{10}^{6}}\\times {{10}^{4}} \\right)}{5.0\\times {{10}^{12}}}[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{13.4945\\times {{10}^{10}}}{5.0\\times {{10}^{12}}}[\/latex]<\/p>\n<p>Regroup using the associative property.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\left( \\frac{13.4945}{5.0} \\right)\\left( \\frac{{{10}^{10}}}{{{10}^{12}}} \\right)[\/latex]<\/p>\n<p>Divide the numbers.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\left(2.6989\\right)\\left(\\frac{10^{10}}{10^{12}}\\right)[\/latex]<\/p>\n<p>Divide the powers of\u00a0[latex]10[\/latex] using the Quotient Rule, so subtract the exponents.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{c}\\left(2.6989 \\right)\\left( {{10}^{10-12}} \\right)\\\\2.6989\\times {{10}^{-2}}\\end{array}[\/latex]<\/p>\n<p>The answer is [latex]2.6989\\times {{10}^{-2}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that when you divide exponential terms, you subtract the exponent in the denominator from the exponent in the numerator. You will see another example of dividing numbers written in scientific notation in the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Writing a Number in Decimal Notation When Given in Scientific Notation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/8BX0oKUMIjw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-795\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Examples: Dividing Numbers Written in Scientific Notation. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/8BX0oKUMIjw\">https:\/\/youtu.be\/8BX0oKUMIjw<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Examples: Multiplying Numbers Written in Scientific Notation. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/5ZAY4OCkp7U\">https:\/\/youtu.be\/5ZAY4OCkp7U<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and 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