{"id":1632,"date":"2021-11-11T20:42:54","date_gmt":"2021-11-11T20:42:54","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=1632"},"modified":"2023-09-15T00:18:10","modified_gmt":"2023-09-15T00:18:10","slug":"1-3-6-exponents-and-square-roots-of-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/1-3-6-exponents-and-square-roots-of-fractions\/","title":{"raw":"1.3.6: Exponents and Square Roots of Fractions","rendered":"1.3.6: Exponents and Square Roots of Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Simplify fractions raised to a power.<\/li>\r\n \t<li>Simplify square roots of fractions.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key words<\/h3>\r\n<ul>\r\n \t<li><strong>Base<\/strong>: The number being raised to a power in an exponential expression<\/li>\r\n \t<li><strong>Exponent<\/strong>:\u00a0The power in an exponential expression<\/li>\r\n \t<li><strong>Principal square root<\/strong>: The positive square root<\/li>\r\n \t<li><strong>Negative square root<\/strong>: The negative square root<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Exponents<\/h2>\r\nExponents are used as a concise way to write multiple multiplication. For example, [latex]2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2=2^{7}[\/latex]. The <em><strong>exponent<\/strong><\/em> [latex]7[\/latex] tells us how many times we have to multiply the <em><strong>base<\/strong><\/em> [latex]2[\/latex] by itself.\r\n\r\nThis same notation is used to raise a fraction to a power.\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\nIdentify the base and the exponent in each term:\r\n\r\n1. [latex]\\left ( \\frac{2}{7}\\right )^{6}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{2}{7}[\/latex] and exponent = [latex]6[\/latex]\r\n\r\n&nbsp;\r\n\r\n2.\u00a0 [latex]\\left ( \\frac{-5}{9}\\right )^{4}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{-5}{9}[\/latex] and exponent = [latex]4[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0 [latex]\\left ( -\\frac{1}{25}\\right )^{3}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]-\\frac{1}{25}[\/latex] and exponent = [latex]3[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nIdentify the base and the exponent in each term:\r\n\r\n1. [latex]\\left ( \\frac{4}{3}\\right )^{5}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{4}{3}[\/latex] and exponent = [latex]5[\/latex]\r\n\r\n&nbsp;\r\n\r\n2.\u00a0 [latex]\\left ( \\frac{-1}{8}\\right )^{7}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{-1}{8}[\/latex] and exponent = [latex]7[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0 [latex]\\left ( -\\frac{11}{5}\\right )^{3}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]-\\frac{11}{5}[\/latex] and exponent = [latex]3[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\n1. [latex]\\left(\\frac{2}{3}\\right )^{2}[\/latex] = [latex]\\frac{2}{3}\\cdot\\frac{2}{3}=\\frac{4}{9}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2. [latex]\\left (\\frac{-1}{2}\\right )^{3}[\/latex] = [latex]\\frac{-1}{2}\\cdot\\frac{-1}{2}\\cdot\\frac{-1}{2}=\\frac{-1}{8}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0 [latex]\\left (-\\frac{3}{4}\\right )^{4}[\/latex] = [latex]-\\frac{3}{4}\\cdot -\\frac{3}{4}\\cdot -\\frac{3}{4}\\cdot -\\frac{3}{4}=\\frac{81}{64}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(\\frac{1}{2}\\right )^{5}=\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}=\\frac{1}{32}[\/latex]<\/span>\r\n\r\n&nbsp;\r\n\r\n5.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(\\frac{-2}{5}\\right )^{3}=\\frac{-2}{5}\\cdot\\frac{-2}{5}\\cdot\\frac{-2}{5}=\\frac{-8}{125}[\/latex]<\/span>\r\n\r\n&nbsp;\r\n\r\n6.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(-\\frac{2}{7}\\right )^{2}=-\\frac{2}{7}\\cdot -\\frac{2}{7}=\\frac{4}{49}[\/latex]<\/span>\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nSimplify by writing the exponential term as multiple multiplication:\r\n\r\n1. [latex]\\left(\\frac{4}{5}\\right )^{2}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2.\u00a0[latex]\\left (\\frac{-2}{5}\\right )^{3}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0[latex]\\left (-\\frac{2}{3}\\right )^{4}[\/latex]\r\n\r\n&nbsp;\r\n\r\n[reveal-answer q=\"796422\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"796422\"]\r\n\r\n1. [latex]\\frac{4}{5}\\cdot\\frac{4}{5}=\\frac{16}{25}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2.\u00a0[latex]\\frac{-2}{5}\\cdot\\frac{-2}{5}\\cdot\\frac{-2}{5}=\\frac{-8}{125}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0[latex]-\\frac{2}{3} \\cdot -\\frac{2}{3}\\cdot -\\frac{2}{3}\\cdot -\\frac{2}{3}=\\frac{16}{81}[\/latex]\r\n\r\n<span style=\"font-size: 1rem; text-align: initial;\">[\/hidden-answer]<\/span>\r\n\r\n<\/div>\r\n<h2>Square Roots<\/h2>\r\nThe <em><strong>principal square root<\/strong><\/em> of a positive integer is the positive number that multiplies by itself to give the integer. As we saw in the section on integers, a positive integer has two square roots. The principal square root is positive and uses the <em><strong>radical sign<\/strong><\/em> for notation. For example, [latex]\\sqrt{4}=2[\/latex]. The integer [latex]4 [\/latex] is a <em><strong>perfect square<\/strong><\/em> since its square root is a whole number. \u00a0[latex]4 [\/latex] also has a negative square root notated with a negative sign in front of the radical:\u00a0[latex]-\\sqrt{4}=-2[\/latex].\r\n\r\nTo find the square root of a fraction, we look for the fraction that squares to give the original fraction.\r\n\r\nFor example, to find the square root of [latex]\\frac{4}{9}[\/latex] we are looking for a fraction that when squared gives us\u00a0[latex]\\frac{4}{9}[\/latex]. Since [latex]2^2 = 4[\/latex] and\u00a0[latex]3^{2} =9[\/latex],\u00a0[latex]\\frac{2^{2}}{3^{2}}=\\frac{4}{9}[\/latex]. Therefore, [latex]\\sqrt{\\frac{4}{9}}=\\frac{2}{3}[\/latex].\r\n\r\nNotice that [latex]\\sqrt{4}=2[\/latex] and [latex]\\sqrt{9}=3[\/latex]. This means that\u00a0[latex]\\sqrt{\\frac{4}{9}}=\\frac{\\sqrt{4}}{\\sqrt{9}}=\\frac{2}{3}[\/latex].\r\n<div class=\"textbox shaded\">\r\n<h3>SQUARE ROOT RULE FOR FRACTIONS<\/h3>\r\n[latex]\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}[\/latex] for any whole numbers [latex]a, b;\\; b \\ne 0[\/latex].\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\nSimplify:\r\n\r\n1. [latex]\\sqrt{\\frac{25}{16}}=\\frac{\\sqrt{25}}{\\sqrt{16}}=\\frac{5}{4}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2. [latex]-\\sqrt{\\frac{81}{4}}=-\\frac{\\sqrt{81}}{\\sqrt{4}}=-\\frac{9}{2}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0[latex]\\sqrt{\\frac{121}{144}}=\\frac{\\sqrt{121}}{\\sqrt{144}}=\\frac{11}{12}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4. [latex]\\sqrt{\\frac{-9}{25}}=\\frac{\\sqrt{-9}}{\\sqrt{25}}[\/latex] is undefined in the set of real numbers\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nSimplify:\r\n\r\n1. [latex]\\sqrt{\\frac{36}{49}}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2. \u00a0[latex]\\sqrt{\\frac{100}{25}}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3. \u00a0[latex]-\\sqrt{\\frac{16}{121}}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4. \u00a0[latex]\\sqrt{\\frac{-16}{81}}[\/latex]\r\n\r\n&nbsp;\r\n\r\n[reveal-answer q=\"558993\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"558993\"]\r\n\r\n1. [latex]\\frac{6}{7}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2. [latex]2[\/latex]\r\n\r\n&nbsp;\r\n\r\n3. [latex]-\\frac{4}{11}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4. Undefined\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Simplify fractions raised to a power.<\/li>\n<li>Simplify square roots of fractions.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key words<\/h3>\n<ul>\n<li><strong>Base<\/strong>: The number being raised to a power in an exponential expression<\/li>\n<li><strong>Exponent<\/strong>:\u00a0The power in an exponential expression<\/li>\n<li><strong>Principal square root<\/strong>: The positive square root<\/li>\n<li><strong>Negative square root<\/strong>: The negative square root<\/li>\n<\/ul>\n<\/div>\n<h2>Exponents<\/h2>\n<p>Exponents are used as a concise way to write multiple multiplication. For example, [latex]2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2\\cdot 2=2^{7}[\/latex]. The <em><strong>exponent<\/strong><\/em> [latex]7[\/latex] tells us how many times we have to multiply the <em><strong>base<\/strong><\/em> [latex]2[\/latex] by itself.<\/p>\n<p>This same notation is used to raise a fraction to a power.<\/p>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>Identify the base and the exponent in each term:<\/p>\n<p>1. [latex]\\left ( \\frac{2}{7}\\right )^{6}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{2}{7}[\/latex] and exponent = [latex]6[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2.\u00a0 [latex]\\left ( \\frac{-5}{9}\\right )^{4}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{-5}{9}[\/latex] and exponent = [latex]4[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0 [latex]\\left ( -\\frac{1}{25}\\right )^{3}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]-\\frac{1}{25}[\/latex] and exponent = [latex]3[\/latex]<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Identify the base and the exponent in each term:<\/p>\n<p>1. [latex]\\left ( \\frac{4}{3}\\right )^{5}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{4}{3}[\/latex] and exponent = [latex]5[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2.\u00a0 [latex]\\left ( \\frac{-1}{8}\\right )^{7}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]\\frac{-1}{8}[\/latex] and exponent = [latex]7[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0 [latex]\\left ( -\\frac{11}{5}\\right )^{3}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Base = [latex]-\\frac{11}{5}[\/latex] and exponent = [latex]3[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>1. [latex]\\left(\\frac{2}{3}\\right )^{2}[\/latex] = [latex]\\frac{2}{3}\\cdot\\frac{2}{3}=\\frac{4}{9}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2. [latex]\\left (\\frac{-1}{2}\\right )^{3}[\/latex] = [latex]\\frac{-1}{2}\\cdot\\frac{-1}{2}\\cdot\\frac{-1}{2}=\\frac{-1}{8}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0 [latex]\\left (-\\frac{3}{4}\\right )^{4}[\/latex] = [latex]-\\frac{3}{4}\\cdot -\\frac{3}{4}\\cdot -\\frac{3}{4}\\cdot -\\frac{3}{4}=\\frac{81}{64}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(\\frac{1}{2}\\right )^{5}=\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}\\cdot\\frac{1}{2}=\\frac{1}{32}[\/latex]<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>5.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(\\frac{-2}{5}\\right )^{3}=\\frac{-2}{5}\\cdot\\frac{-2}{5}\\cdot\\frac{-2}{5}=\\frac{-8}{125}[\/latex]<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>6.\u00a0<span style=\"font-size: 1em;\">[latex]\\left(-\\frac{2}{7}\\right )^{2}=-\\frac{2}{7}\\cdot -\\frac{2}{7}=\\frac{4}{49}[\/latex]<\/span><\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Simplify by writing the exponential term as multiple multiplication:<\/p>\n<p>1. [latex]\\left(\\frac{4}{5}\\right )^{2}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2.\u00a0[latex]\\left (\\frac{-2}{5}\\right )^{3}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0[latex]\\left (-\\frac{2}{3}\\right )^{4}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q796422\">Show Answer<\/span><\/p>\n<div id=\"q796422\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. [latex]\\frac{4}{5}\\cdot\\frac{4}{5}=\\frac{16}{25}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2.\u00a0[latex]\\frac{-2}{5}\\cdot\\frac{-2}{5}\\cdot\\frac{-2}{5}=\\frac{-8}{125}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0[latex]-\\frac{2}{3} \\cdot -\\frac{2}{3}\\cdot -\\frac{2}{3}\\cdot -\\frac{2}{3}=\\frac{16}{81}[\/latex]<\/p>\n<p><span style=\"font-size: 1rem; text-align: initial;\"><\/div>\n<\/div>\n<p><\/span><\/p>\n<\/div>\n<h2>Square Roots<\/h2>\n<p>The <em><strong>principal square root<\/strong><\/em> of a positive integer is the positive number that multiplies by itself to give the integer. As we saw in the section on integers, a positive integer has two square roots. The principal square root is positive and uses the <em><strong>radical sign<\/strong><\/em> for notation. For example, [latex]\\sqrt{4}=2[\/latex]. The integer [latex]4[\/latex] is a <em><strong>perfect square<\/strong><\/em> since its square root is a whole number. \u00a0[latex]4[\/latex] also has a negative square root notated with a negative sign in front of the radical:\u00a0[latex]-\\sqrt{4}=-2[\/latex].<\/p>\n<p>To find the square root of a fraction, we look for the fraction that squares to give the original fraction.<\/p>\n<p>For example, to find the square root of [latex]\\frac{4}{9}[\/latex] we are looking for a fraction that when squared gives us\u00a0[latex]\\frac{4}{9}[\/latex]. Since [latex]2^2 = 4[\/latex] and\u00a0[latex]3^{2} =9[\/latex],\u00a0[latex]\\frac{2^{2}}{3^{2}}=\\frac{4}{9}[\/latex]. Therefore, [latex]\\sqrt{\\frac{4}{9}}=\\frac{2}{3}[\/latex].<\/p>\n<p>Notice that [latex]\\sqrt{4}=2[\/latex] and [latex]\\sqrt{9}=3[\/latex]. This means that\u00a0[latex]\\sqrt{\\frac{4}{9}}=\\frac{\\sqrt{4}}{\\sqrt{9}}=\\frac{2}{3}[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>SQUARE ROOT RULE FOR FRACTIONS<\/h3>\n<p>[latex]\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}[\/latex] for any whole numbers [latex]a, b;\\; b \\ne 0[\/latex].<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]\\sqrt{\\frac{25}{16}}=\\frac{\\sqrt{25}}{\\sqrt{16}}=\\frac{5}{4}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2. [latex]-\\sqrt{\\frac{81}{4}}=-\\frac{\\sqrt{81}}{\\sqrt{4}}=-\\frac{9}{2}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0[latex]\\sqrt{\\frac{121}{144}}=\\frac{\\sqrt{121}}{\\sqrt{144}}=\\frac{11}{12}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4. [latex]\\sqrt{\\frac{-9}{25}}=\\frac{\\sqrt{-9}}{\\sqrt{25}}[\/latex] is undefined in the set of real numbers<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]\\sqrt{\\frac{36}{49}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2. \u00a0[latex]\\sqrt{\\frac{100}{25}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3. \u00a0[latex]-\\sqrt{\\frac{16}{121}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4. \u00a0[latex]\\sqrt{\\frac{-16}{81}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q558993\">Show Answer<\/span><\/p>\n<div id=\"q558993\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. [latex]\\frac{6}{7}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2. [latex]2[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3. [latex]-\\frac{4}{11}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4. Undefined<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/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-1632\">\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>1.3.6: Exponents and Square Roots of Fractions. <strong>Authored by<\/strong>: Hazel McKenna. <strong>Provided by<\/strong>: Utah Valley University. <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":370291,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"1.3.6: Exponents and Square Roots of Fractions\",\"author\":\"Hazel McKenna\",\"organization\":\"Utah Valley University\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1632","chapter","type-chapter","status-publish","hentry"],"part":587,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/users\/370291"}],"version-history":[{"count":25,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1632\/revisions"}],"predecessor-version":[{"id":2737,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1632\/revisions\/2737"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/parts\/587"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1632\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/media?parent=1632"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1632"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/contributor?post=1632"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/license?post=1632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}