{"id":4686,"date":"2017-06-07T18:55:17","date_gmt":"2017-06-07T18:55:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-negative-and-zero-exponent-rules\/"},"modified":"2017-08-15T15:39:24","modified_gmt":"2017-08-15T15:39:24","slug":"read-negative-and-zero-exponent-rules","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-negative-and-zero-exponent-rules\/","title":{"raw":"Negative and Zero Exponent Rules","rendered":"Negative and Zero Exponent Rules"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define and use the zero exponent rule<\/li>\r\n \t<li>Define and use the negative exponent rule<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Define and use the zero exponent rule<\/h2>\r\nWhen we defined the quotient rule, we only worked with expressions like the following: [latex]\\frac{{{4}^{9}}}{{{4}^{4}}}[\/latex], where the exponent in the numerator (up) was greater than the one in the denominator (down), so the final exponent after simplifying was always a positive number, and greater than zero. In this section, we will explore what happens when we apply the quotient rule for exponents and get a negative or zero exponent.\r\n<h2><span style=\"color: #4c8bb0\">What if the exponent is zero?<\/span><\/h2>\r\nTo see how this is defined, let us begin with an example. We will use the idea that dividing any number by itself gives a result of 1.\r\n<p style=\"text-align: center\">[latex]\\frac{t^{8}}{t^{8}}=\\frac{\\cancel{t^{8}}}{\\cancel{t^{8}}}=1[\/latex]<\/p>\r\nIf we were to simplify the original expression using the quotient rule, we would have\r\n<p style=\"text-align: center\">[latex]\\frac{{t}^{8}}{{t}^{8}}={t}^{8 - 8}={t}^{0}[\/latex]<\/p>\r\nIf we equate the two answers, the result is [latex]{t}^{0}=1[\/latex]. This is true for any nonzero real number, or any variable representing a real number.\r\n<div style=\"text-align: center\">[latex]{a}^{0}=1[\/latex]<\/div>\r\nThe sole exception is the expression [latex]{0}^{0}[\/latex]. This appears later in more advanced courses, but for now, we will consider the value to be undefined, or DNE (Does Not Exist).\r\n<div class=\"textbox shaded\">\r\n<h3>Exponents of 0 or 1<\/h3>\r\nAny number or variable raised to a power of 1 is the number itself.\r\n<p style=\"text-align: center\">[latex]n^{1}=n[\/latex]<\/p>\r\nAny non-zero number or variable raised to a power of 0 is equal to 1\r\n<p style=\"text-align: center\">[latex]n^{0}=1[\/latex]<\/p>\r\nThe quantity [latex]0^{0}[\/latex]\u00a0is undefined.\r\n\r\n<\/div>\r\nAs done previously, to evaluate expressions containing exponents of 0 or 1, substitute the value of the variable into the expression and simplify.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]2x^{0}[\/latex] if [latex]x=9[\/latex]\r\n\r\n[reveal-answer q=\"324798\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"324798\"]Substitute 9 for the variable <i>x<\/i>.\r\n<p style=\"text-align: center\">[latex]2\\cdot9^{0}[\/latex]<\/p>\r\nEvaluate [latex]9^{0}[\/latex]. Multiply.\r\n<p style=\"text-align: center\">[latex]2\\cdot1=2[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]2x^{0}=2[\/latex], if [latex]x=9[\/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\nSimplify\u00a0[latex]\\frac{{c}^{3}}{{c}^{3}}[\/latex].\r\n\r\n[reveal-answer q=\"769979\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"769979\"]Use the quotient and zero exponent rules to simplify the\u00a0expression.\r\n<p style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{c^{3}}{c^{3}} \\,\\,\\,= \\,\\,\\,c^{3-3} \\\\ \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,c^{0} \\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,1\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n1\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video there is an example of evaluating an expression with an exponent of zero, as well as simplifying when you get a result of a zero exponent.\r\n\r\nhttps:\/\/youtu.be\/jKihp_DVDa0\r\n<h2>Define and use the negative exponent rule<\/h2>\r\nWe proposed another question at the beginning of this section.\u00a0 Given a quotient like\u00a0[latex] \\displaystyle \\frac{{{2}^{m}}}{{{2}^{n}}}[\/latex] what happens when <em>n<\/em> is larger than <em>m<\/em>? We will need to use the <em>negative rule of exponents<\/em> to simplify the expression so that it is easier to understand.\r\n\r\nLet's look at an example to clarify this idea. Given the expression:\r\n<p style=\"text-align: center\">[latex]\\frac{{h}^{3}}{{h}^{5}}[\/latex]<\/p>\r\nExpand the numerator and denominator, all the terms in the numerator will cancel to 1, leaving two <em>h<\/em>s multiplied in the denominator, and a numerator of 1.\r\n<div style=\"text-align: center\">[latex]\\begin{array}{l} \\frac{{h}^{3}}{{h}^{5}}\\,\\,\\,=\\,\\,\\,\\frac{h\\cdot{h}\\cdot{h}}{h\\cdot{h}\\cdot{h}\\cdot{h}\\cdot{h}} \\\\ \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{\\cancel{h}\\cdot \\cancel{h}\\cdot \\cancel{h}}{\\cancel{h}\\cdot \\cancel{h}\\cdot \\cancel{h}\\cdot {h}\\cdot {h}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{1}{h\\cdot{h}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{1}{{h}^{2}} \\end{array}[\/latex]<\/div>\r\nWe could have also applied the quotient rule from the last section, to obtain the following result:\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{h^{3}}{h^{5}}\\,\\,\\,=\\,\\,\\,h^{3-5}\\\\\\\\=\\,\\,\\,h^{-2}\\,\\,\\end{array}[\/latex]<\/p>\r\nPutting the answers together, we have [latex]{h}^{-2}=\\frac{1}{{h}^{2}}[\/latex]. This is true when <em>h<\/em>, or any variable, is a real number and is not zero.\r\n<div class=\"textbox shaded\">\r\n<h3>The Negative Rule of Exponents<\/h3>\r\nFor any nonzero real number [latex]a[\/latex] and natural number [latex]n[\/latex], the negative rule of exponents states that\r\n<div style=\"text-align: center\">[latex]{a}^{-n}=\\frac{1}{{a}^{n}}[\/latex]<\/div>\r\n<\/div>\r\nLet's looks at some examples of how this rule applies under different circumstances.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\n<p style=\"text-align: left\">Evaluate the expression [latex]{4}^{-3}[\/latex].<\/p>\r\n<p style=\"text-align: left\">[reveal-answer q=\"231258\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"231258\"]First, write the expression with positive exponents by putting the term with the negative exponent in the denominator.<\/p>\r\n<p style=\"text-align: center\">[latex]{4}^{-3} = \\frac{1}{{4}^{3}} = \\frac{1}{4\\cdot4\\cdot4}[\/latex]<\/p>\r\nNow that we have an expression that looks somewhat familiar.\r\n<p style=\"text-align: center\">[latex]\\frac{1}{4\\cdot4\\cdot4} = \\frac{1}{64}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]\\frac{1}{64}[\/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\nWrite [latex]\\frac{{\\left({t}^{3}\\right)}}{{\\left({t}^{8}\\right)}}[\/latex] with positive exponents.\r\n<p style=\"text-align: left\">[reveal-answer q=\"219981\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"219981\"]<\/p>\r\n<p style=\"text-align: left\">Use the quotient rule to subtract the exponents of terms with like bases.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{{\\left({t}^{3}\\right)}}{{\\left({t}^{8}\\right)}}={t}^{3-8}\\\\={t}^{-5}\\,\\,\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">Write the expression with positive exponents by putting the term with the negative exponent in the denominator.<\/p>\r\n<p style=\"text-align: center\">[latex]=\\frac{1}{{t}^{5}}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]\\frac{1}{{t}^{5}}[\/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\nSimplify [latex]{\\left(\\frac{1}{3}\\right)}^{-2}[\/latex].\r\n\r\n[reveal-answer q=\"998337\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"998337\"]Apply the power property of exponents.\r\n<p style=\"text-align: center\">[latex]\\frac{{1}^{-2}}{{3}^{-2}}[\/latex]<\/p>\r\nWrite each term with a positive exponent, the numerator will go to the denominator and the denominator will go to the numerator.\r\n<p style=\"text-align: center\">[latex]\\frac{{3}^{2}}{{1}^{2}}{ = }\\frac{{3}\\cdot{3}}{{1}\\cdot{1}}[\/latex]<\/p>\r\nSimplify.\r\n<p style=\"text-align: center\">[latex]\\frac{{3}\\cdot{3}}{{1}\\cdot{1}}{ = }\\frac{9}{1}{ = }{9}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]9[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify.[latex]\\frac{1}{4^{-2}}[\/latex] Write your answer using positive exponents.\r\n\r\n[reveal-answer q=\"629171\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"629171\"]\r\n\r\nWrite each term with a positive exponent, the denominator will go to the numerator.\r\n<p style=\"text-align: center\">[latex]\\frac{1}{4^{-2}}=1\\cdot\\frac{4^{2}}{1}=\\frac{16}{1}=16[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n16\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the follwoing video you will see examples of simplifying expressions with negative exponents.\r\n\r\nhttps:\/\/youtu.be\/WvFlHjlIITg","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define and use the zero exponent rule<\/li>\n<li>Define and use the negative exponent rule<\/li>\n<\/ul>\n<\/div>\n<h2>Define and use the zero exponent rule<\/h2>\n<p>When we defined the quotient rule, we only worked with expressions like the following: [latex]\\frac{{{4}^{9}}}{{{4}^{4}}}[\/latex], where the exponent in the numerator (up) was greater than the one in the denominator (down), so the final exponent after simplifying was always a positive number, and greater than zero. In this section, we will explore what happens when we apply the quotient rule for exponents and get a negative or zero exponent.<\/p>\n<h2><span style=\"color: #4c8bb0\">What if the exponent is zero?<\/span><\/h2>\n<p>To see how this is defined, let us begin with an example. We will use the idea that dividing any number by itself gives a result of 1.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{t^{8}}{t^{8}}=\\frac{\\cancel{t^{8}}}{\\cancel{t^{8}}}=1[\/latex]<\/p>\n<p>If we were to simplify the original expression using the quotient rule, we would have<\/p>\n<p style=\"text-align: center\">[latex]\\frac{{t}^{8}}{{t}^{8}}={t}^{8 - 8}={t}^{0}[\/latex]<\/p>\n<p>If we equate the two answers, the result is [latex]{t}^{0}=1[\/latex]. This is true for any nonzero real number, or any variable representing a real number.<\/p>\n<div style=\"text-align: center\">[latex]{a}^{0}=1[\/latex]<\/div>\n<p>The sole exception is the expression [latex]{0}^{0}[\/latex]. This appears later in more advanced courses, but for now, we will consider the value to be undefined, or DNE (Does Not Exist).<\/p>\n<div class=\"textbox shaded\">\n<h3>Exponents of 0 or 1<\/h3>\n<p>Any number or variable raised to a power of 1 is the number itself.<\/p>\n<p style=\"text-align: center\">[latex]n^{1}=n[\/latex]<\/p>\n<p>Any non-zero number or variable raised to a power of 0 is equal to 1<\/p>\n<p style=\"text-align: center\">[latex]n^{0}=1[\/latex]<\/p>\n<p>The quantity [latex]0^{0}[\/latex]\u00a0is undefined.<\/p>\n<\/div>\n<p>As done previously, to evaluate expressions containing exponents of 0 or 1, substitute the value of the variable into the expression and simplify.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]2x^{0}[\/latex] if [latex]x=9[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q324798\">Show Solution<\/span><\/p>\n<div id=\"q324798\" class=\"hidden-answer\" style=\"display: none\">Substitute 9 for the variable <i>x<\/i>.<\/p>\n<p style=\"text-align: center\">[latex]2\\cdot9^{0}[\/latex]<\/p>\n<p>Evaluate [latex]9^{0}[\/latex]. Multiply.<\/p>\n<p style=\"text-align: center\">[latex]2\\cdot1=2[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]2x^{0}=2[\/latex], if [latex]x=9[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify\u00a0[latex]\\frac{{c}^{3}}{{c}^{3}}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q769979\">Show Solution<\/span><\/p>\n<div id=\"q769979\" class=\"hidden-answer\" style=\"display: none\">Use the quotient and zero exponent rules to simplify the\u00a0expression.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{c^{3}}{c^{3}} \\,\\,\\,= \\,\\,\\,c^{3-3} \\\\ \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,c^{0} \\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,1\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>1<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video there is an example of evaluating an expression with an exponent of zero, as well as simplifying when you get a result of a zero exponent.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Evaluate and Simplify Expressions Using the Zero Exponent Rule\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jKihp_DVDa0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Define and use the negative exponent rule<\/h2>\n<p>We proposed another question at the beginning of this section.\u00a0 Given a quotient like\u00a0[latex]\\displaystyle \\frac{{{2}^{m}}}{{{2}^{n}}}[\/latex] what happens when <em>n<\/em> is larger than <em>m<\/em>? We will need to use the <em>negative rule of exponents<\/em> to simplify the expression so that it is easier to understand.<\/p>\n<p>Let&#8217;s look at an example to clarify this idea. Given the expression:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{{h}^{3}}{{h}^{5}}[\/latex]<\/p>\n<p>Expand the numerator and denominator, all the terms in the numerator will cancel to 1, leaving two <em>h<\/em>s multiplied in the denominator, and a numerator of 1.<\/p>\n<div style=\"text-align: center\">[latex]\\begin{array}{l} \\frac{{h}^{3}}{{h}^{5}}\\,\\,\\,=\\,\\,\\,\\frac{h\\cdot{h}\\cdot{h}}{h\\cdot{h}\\cdot{h}\\cdot{h}\\cdot{h}} \\\\ \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{\\cancel{h}\\cdot \\cancel{h}\\cdot \\cancel{h}}{\\cancel{h}\\cdot \\cancel{h}\\cdot \\cancel{h}\\cdot {h}\\cdot {h}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{1}{h\\cdot{h}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\,\\,\\,\\frac{1}{{h}^{2}} \\end{array}[\/latex]<\/div>\n<p>We could have also applied the quotient rule from the last section, to obtain the following result:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{h^{3}}{h^{5}}\\,\\,\\,=\\,\\,\\,h^{3-5}\\\\\\\\=\\,\\,\\,h^{-2}\\,\\,\\end{array}[\/latex]<\/p>\n<p>Putting the answers together, we have [latex]{h}^{-2}=\\frac{1}{{h}^{2}}[\/latex]. This is true when <em>h<\/em>, or any variable, is a real number and is not zero.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Negative Rule of Exponents<\/h3>\n<p>For any nonzero real number [latex]a[\/latex] and natural number [latex]n[\/latex], the negative rule of exponents states that<\/p>\n<div style=\"text-align: center\">[latex]{a}^{-n}=\\frac{1}{{a}^{n}}[\/latex]<\/div>\n<\/div>\n<p>Let&#8217;s looks at some examples of how this rule applies under different circumstances.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p style=\"text-align: left\">Evaluate the expression [latex]{4}^{-3}[\/latex].<\/p>\n<p style=\"text-align: left\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q231258\">Show Solution<\/span><\/p>\n<div id=\"q231258\" class=\"hidden-answer\" style=\"display: none\">First, write the expression with positive exponents by putting the term with the negative exponent in the denominator.<\/p>\n<p style=\"text-align: center\">[latex]{4}^{-3} = \\frac{1}{{4}^{3}} = \\frac{1}{4\\cdot4\\cdot4}[\/latex]<\/p>\n<p>Now that we have an expression that looks somewhat familiar.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{1}{4\\cdot4\\cdot4} = \\frac{1}{64}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\frac{1}{64}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Write [latex]\\frac{{\\left({t}^{3}\\right)}}{{\\left({t}^{8}\\right)}}[\/latex] with positive exponents.<\/p>\n<p style=\"text-align: left\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q219981\">Show Solution<\/span><\/p>\n<div id=\"q219981\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: left\">Use the quotient rule to subtract the exponents of terms with like bases.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{{\\left({t}^{3}\\right)}}{{\\left({t}^{8}\\right)}}={t}^{3-8}\\\\={t}^{-5}\\,\\,\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">Write the expression with positive exponents by putting the term with the negative exponent in the denominator.<\/p>\n<p style=\"text-align: center\">[latex]=\\frac{1}{{t}^{5}}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\frac{1}{{t}^{5}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify [latex]{\\left(\\frac{1}{3}\\right)}^{-2}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q998337\">Show Solution<\/span><\/p>\n<div id=\"q998337\" class=\"hidden-answer\" style=\"display: none\">Apply the power property of exponents.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{{1}^{-2}}{{3}^{-2}}[\/latex]<\/p>\n<p>Write each term with a positive exponent, the numerator will go to the denominator and the denominator will go to the numerator.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{{3}^{2}}{{1}^{2}}{ = }\\frac{{3}\\cdot{3}}{{1}\\cdot{1}}[\/latex]<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{{3}\\cdot{3}}{{1}\\cdot{1}}{ = }\\frac{9}{1}{ = }{9}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]9[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify.[latex]\\frac{1}{4^{-2}}[\/latex] Write your answer using positive exponents.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q629171\">Show Solution<\/span><\/p>\n<div id=\"q629171\" class=\"hidden-answer\" style=\"display: none\">\n<p>Write each term with a positive exponent, the denominator will go to the numerator.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{1}{4^{-2}}=1\\cdot\\frac{4^{2}}{1}=\\frac{16}{1}=16[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>16<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the follwoing video you will see examples of simplifying expressions with negative exponents.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Negative Exponents - Basics\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/WvFlHjlIITg?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-4686\">\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><li>Evaluate and Simplify Expressions Using the Zero Exponent Rule Mathispower4u  Mathispower4u. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jKihp_DVDa0\">https:\/\/youtu.be\/jKihp_DVDa0<\/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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Jay Abrams et, al.. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/\">https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/<\/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>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>Ex: Negative Exponents - 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