{"id":16225,"date":"2019-10-01T22:23:42","date_gmt":"2019-10-01T22:23:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-terms-and-expressions-with-exponents\/"},"modified":"2024-04-30T21:31:46","modified_gmt":"2024-04-30T21:31:46","slug":"read-terms-and-expressions-with-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-terms-and-expressions-with-exponents\/","title":{"raw":"Evaluating Exponential Expressions","rendered":"Evaluating Exponential Expressions"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Evaluate exponential expressions<\/li>\r\n<\/ul>\r\n<\/div>\r\n\r\n[caption id=\"attachment_4445\" align=\"aligncenter\" width=\"282\"]<img class=\"wp-image-4445 \" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/05\/31173815\/Screen-Shot-2016-05-31-at-10.38.21-AM-150x150.png\" alt=\"Image of a woman taking a picture with a camera repeated five times in different colors.\" width=\"282\" height=\"282\" \/> Repeated Image[\/caption]\r\n<h2>Anatomy of exponential\u00a0terms<\/h2>\r\nWe use exponential notation to write repeated multiplication of the same quantity. For example, [latex]{2}^{4}[\/latex] means to multiply four factors of [latex]2[\/latex], so [latex]{2}^{4}[\/latex] means [latex]2\\cdot 2\\cdot 2\\cdot 2[\/latex].\u00a0 Conversely, [latex]10\\cdot10\\cdot10[\/latex] can be written more succinctly as [latex]10^{3}[\/latex]. The [latex]10[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>base<\/b>. The [latex]3[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>exponent<\/b>. The expression [latex]10^{3}[\/latex] is called the exponential expression. Knowing the names for the parts of an exponential expression or term will help you learn how to perform mathematical operations on them.\r\n<div class=\"textbox shaded\">\r\n<h3>Exponential Notation<\/h3>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224353\/CNX_BMath_Figure_10_02_013_img.png\" alt=\"On the left side, a raised to the m is shown. The m is labeled in blue as an exponent. The a is labeled in red as the base. On the right, it says a to the m means multiply m factors of a. Below this, it says a to the m equals a times a times a times a, with m factors written below in blue.\" \/>\r\nThis is read [latex]a[\/latex] to the [latex]{m}^{\\mathrm{th}}[\/latex] power.\r\n\r\n<\/div>\r\nIn the expression [latex]{a}^{m}[\/latex], the exponent tells us how many times we use the base [latex]a[\/latex] as a factor.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224355\/CNX_BMath_Figure_10_02_014_img.png\" alt=\"On the left side, 7 to the 3rd power is shown. Below is 7 times 7 times 7, with 3 factors written below. On the right side, parentheses negative 8 to the 5th power is shown. Below is negative 8 times negative 8 times negative 8 times negative 8 times negative 8, with 5 factors written below.\" \/>\r\n\r\n[latex]10^{3}[\/latex] is read as \u201c[latex]10[\/latex] to the third power\u201d or \u201c[latex]10[\/latex] cubed.\u201d It means [latex]10\\cdot10\\cdot10[\/latex], or [latex]1,000[\/latex].\r\n\r\n[latex]8^{2}[\/latex]\u00a0is read as \u201c[latex]8[\/latex] to the second power\u201d or \u201c[latex]8[\/latex] squared.\u201d It means [latex]8\\cdot8[\/latex], or [latex]64[\/latex].\r\n\r\n[latex]5^{4}[\/latex]\u00a0is read as \u201c[latex]5[\/latex] to the fourth power.\u201d It means [latex]5\\cdot5\\cdot5\\cdot5[\/latex], or [latex]625[\/latex].\r\n\r\n[latex]b^{5}[\/latex]\u00a0is read as \u201cb to the fifth power.\u201d It means [latex]{b}\\cdot{b}\\cdot{b}\\cdot{b}\\cdot{b}[\/latex]. Its value will depend on the value of b.\r\n\r\nThe exponent applies only to the number that it is next to. Therefore, in the expression [latex]xy^{4}[\/latex],\u00a0only the [latex]y[\/latex] is affected by the [latex]4[\/latex]. [latex]xy^{4}[\/latex]\u00a0means [latex]{x}\\cdot{y}\\cdot{y}\\cdot{y}\\cdot{y}[\/latex].\r\n\r\nIf the exponential expression is negative, such as [latex]\u22123^{4}[\/latex], it means [latex]\u2013\\left(3\\cdot3\\cdot3\\cdot3\\right)[\/latex] or [latex]\u221281[\/latex].\r\n\r\nIf [latex]\u22123[\/latex] is to be the base, it must be written as [latex]\\left(\u22123\\right)^{4}[\/latex], which means [latex]\u22123\\cdot\u22123\\cdot\u22123\\cdot\u22123[\/latex], or [latex]81[\/latex].\r\n\r\nLikewise,\u00a0[latex]\\left(\u2212x\\right)^{4}=\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)=x^{4}[\/latex], while [latex]\u2212x^{4}=\u2013\\left(x\\cdot x\\cdot x\\cdot x\\right)[\/latex].\r\n\r\nYou can see that there is quite a difference, so you have to be very careful! The following examples show how to identify the base and the exponent, as well as how to identify the expanded and exponential format of writing repeated multiplication.\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIdentify the exponent and the base in the following terms, then simplify:\r\n<ol>\r\n \t<li>[latex]7^{2}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(\\frac{1}{2}\\right)}^{3}[\/latex]<\/li>\r\n \t<li>[latex]2x^{3}[\/latex]<\/li>\r\n \t<li>[latex]\\left(-5\\right)^{2}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"211363\"]Show Solution[\/reveal-answer]\r\n<p style=\"text-align: left;\">[hidden-answer a=\"211363\"]<\/p>\r\n1) [latex]7^{2}[\/latex]\r\n\r\nThe exponent in this term is [latex]2[\/latex] and the base is [latex]7[\/latex]. To simplify, expand the term: [latex]7^{2}=7\\cdot{7}=49[\/latex]\r\n\r\n2) [latex]{\\left(\\frac{1}{2}\\right)}^{3}[\/latex]\r\n\r\nThe exponent on this term is [latex]3[\/latex], and the base is [latex]\\frac{1}{2}[\/latex]. To simplify, expand the multiplication and remember how to multiply fractions: [latex]{\\left(\\frac{1}{2}\\right)}^{3}=\\frac{1}{2}\\cdot{\\frac{1}{2}}\\cdot{\\frac{1}{2}}=\\frac{1}{8}[\/latex]\r\n\r\n3) \u00a0[latex]2x^{3}[\/latex]\r\n\r\nThe exponent on this term is [latex]3[\/latex], and the base is [latex]x[\/latex], the [latex]2[\/latex] is not getting the exponent because there are no parentheses that tell us it is. \u00a0This term is in its most simplified form.\r\n\r\n4)\u00a0[latex]\\left(-5\\right)^{2}[\/latex]\r\n\r\nThe exponent on this terms is [latex]2[\/latex] and the base is [latex]-5[\/latex]. To simplify, expand the multiplication: [latex]\\left(-5\\right)^{2}=-5\\cdot{-5}=25[\/latex]\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<p class=\"no-indent\">In the following video you are provided more examples of applying exponents to various bases.<\/p>\r\nhttps:\/\/youtu.be\/ocedY91LHKU\r\n\r\nBefore we begin working with variable expressions containing exponents, let\u2019s simplify a few expressions involving only numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n\r\n1. [latex]{5}^{3}[\/latex]\r\n2. [latex]{9}^{1}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168469452397\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{5}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply [latex]3[\/latex] factors of [latex]5[\/latex].<\/td>\r\n<td>[latex]5\\cdot 5\\cdot 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]125[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168046009892\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{9}^{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply [latex]1[\/latex] factor of [latex]9[\/latex].<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146094[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n\r\n1. [latex]{\\left({\\Large\\frac{7}{8}}\\right)}^{2}[\/latex]\r\n2. [latex]{\\left(0.74\\right)}^{2}[\/latex]\r\n[reveal-answer q=\"153461\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"153461\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469451188\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\">1.<\/td>\r\n<td style=\"height: 15px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.2334px;\">\r\n<td style=\"height: 15.2334px;\"><\/td>\r\n<td style=\"height: 15.2334px;\">[latex]{\\left({\\Large\\frac{7}{8}}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\">Multiply two factors.<\/td>\r\n<td style=\"height: 15px;\">[latex]\\left({\\Large\\frac{7}{8}}\\right)\\left({\\Large\\frac{7}{8}}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\">Simplify.<\/td>\r\n<td style=\"height: 15px;\">[latex]{\\Large\\frac{49}{64}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168047561610\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(0.74\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply two factors.<\/td>\r\n<td>[latex]\\left(0.74\\right)\\left(0.74\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]0.5476[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146095[\/ohm_question]\r\n\r\n[ohm_question]146867[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n\r\n1. [latex]{\\left(-3\\right)}^{4}[\/latex]\r\n2. [latex]{-3}^{4}[\/latex]\r\n[reveal-answer q=\"152453\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"152453\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468562526\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(-3\\right)}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply four factors of [latex]\u22123[\/latex].<\/td>\r\n<td>[latex]\\left(-3\\right)\\left(-3\\right)\\left(-3\\right)\\left(-3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]81[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168048408997\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{-3}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply two factors.<\/td>\r\n<td>[latex]-\\left(3\\cdot 3\\cdot 3\\cdot 3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-81[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice the similarities and differences in parts 1 and 2. Why are the answers different? In part 1 the parentheses tell us to raise the [latex](\u22123)[\/latex] to the [latex]4[\/latex]<sup>th<\/sup> power. In part 2 we raise only the [latex]3[\/latex] to the [latex]4[\/latex]<sup>th<\/sup> power and then find the opposite.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146097[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Evaluate expressions<\/h3>\r\nEvaluating expressions containing exponents is the same as evaluating the linear expressions from earlier in the course. You substitute the value of the variable into the expression and simplify.\r\n\r\nYou can use the order of operations\u00a0to evaluate the expressions containing exponents. First, evaluate anything in Parentheses or grouping symbols. Next, look for Exponents, followed by Multiplication and Division (reading from left to right), and lastly, Addition and Subtraction (again, reading from left to right).\r\n\r\nSo, when you evaluate the expression [latex]5x^{3}[\/latex]\u00a0if [latex]x=4[\/latex], first substitute the value [latex]4[\/latex] for the variable [latex]x[\/latex]. Then evaluate, using order of operations.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate\u00a0[latex]5x^{3}[\/latex]\u00a0if [latex]x=4[\/latex].\r\n\r\n[reveal-answer q=\"411363\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"411363\"]\r\n\r\nSubstitute [latex]4[\/latex] for the variable [latex]x[\/latex].\r\n<p style=\"text-align: center;\">[latex]5\\cdot4^{3}[\/latex]<\/p>\r\nEvaluate [latex]4^{3}[\/latex]. Multiply.\r\n<p style=\"text-align: center;\">[latex]5\\left(4\\cdot4\\cdot4\\right)=5\\cdot64=320[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]5x^{3}=320[\/latex]\u00a0when [latex]x=4[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the example below, notice how adding parentheses can change the outcome when you are simplifying terms with exponents.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]\\left(5x\\right)^{3}[\/latex]\u00a0if [latex]x=4[\/latex].\r\n\r\n[reveal-answer q=\"362021\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"362021\"]Substitute [latex]4[\/latex] for the variable [latex]x[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\left(5\\cdot4\\right)3[\/latex]<\/p>\r\nMultiply inside the parentheses, then apply the exponent\u2014following the rules of PEMDAS.\r\n<p style=\"text-align: center;\">[latex]20^{3}[\/latex]<\/p>\r\nEvaluate [latex]20^{3}[\/latex].\r\n<p style=\"text-align: center;\">[latex]20\\cdot20\\cdot20=8,000[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]\\left(5x\\right)3=8,000[\/latex] when [latex]x=4[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe addition of parentheses made quite a difference!\u00a0Parentheses allow you to apply an exponent to variables or numbers that are multiplied, divided, added, or subtracted to each other.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]53024[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]x^{3}[\/latex] if [latex]x=\u22124[\/latex].\r\n\r\n[reveal-answer q=\"86290\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"86290\"]Substitute [latex]\u22124[\/latex] for the variable x.\r\n<p style=\"text-align: center;\">[latex]\\left(\u22124\\right)^{3}[\/latex]<\/p>\r\nEvaluate. Note how placing parentheses around the [latex]\u22124[\/latex] means the negative sign also gets multiplied.\r\n<p style=\"text-align: center;\">[latex]\u22124\\cdot\u22124\\cdot\u22124[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex]\u22124\\cdot\u22124\\cdot\u22124=\u221264[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x^{3}=\u221264[\/latex] when [latex]x=\u22124[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n\r\n<img class=\"wp-image-2132 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/22011815\/traffic-sign-160659-300x265.png\" alt=\"Caution\" width=\"75\" height=\"66\" \/>\r\n\r\nCaution! Whether to include a negative sign as part of a base or not often leads to confusion. To clarify\u00a0whether a negative sign is applied before or after the exponent, here is an example.\r\n\r\n&nbsp;\r\n\r\nWhat is the difference in the way you would evaluate these two terms?\r\n<ol>\r\n \t<li style=\"text-align: left;\">[latex]-{3}^{2}[\/latex]<\/li>\r\n \t<li style=\"text-align: left;\">[latex]{\\left(-3\\right)}^{2}[\/latex]<\/li>\r\n<\/ol>\r\nTo evaluate 1), you would apply the exponent to the three first, then apply the negative sign last, like this:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}-\\left({3}^{2}\\right)\\\\=-\\left(9\\right) = -9\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">To evaluate 2), you would apply the exponent to the [latex]3[\/latex] and the negative sign:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}{\\left(-3\\right)}^{2}\\\\=\\left(-3\\right)\\cdot\\left(-3\\right)\\\\={ 9}\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">The key to remembering this is to follow the order of operations. The first expression does not include parentheses so you would apply the exponent to the integer [latex]3[\/latex] first, then apply the negative sign. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared.<\/p>\r\n\r\n<\/div>\r\n<p id=\"video0\" class=\"no-indent\" style=\"text-align: left;\">In the next sections, you will learn how to simplify expressions that contain exponents. Come back to this page if you forget how to apply the order of operations to a term with exponents, or forget which is the base and which is the exponent!<\/p>\r\n<p class=\"no-indent\" style=\"text-align: left;\">In the following video you are provided with examples of evaluating exponential expressions for a given number.<\/p>\r\nhttps:\/\/youtu.be\/pQNz8IpVVg0\r\n","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate exponential expressions<\/li>\n<\/ul>\n<\/div>\n<div id=\"attachment_4445\" style=\"width: 292px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4445\" class=\"wp-image-4445\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/05\/31173815\/Screen-Shot-2016-05-31-at-10.38.21-AM-150x150.png\" alt=\"Image of a woman taking a picture with a camera repeated five times in different colors.\" width=\"282\" height=\"282\" \/><\/p>\n<p id=\"caption-attachment-4445\" class=\"wp-caption-text\">Repeated Image<\/p>\n<\/div>\n<h2>Anatomy of exponential\u00a0terms<\/h2>\n<p>We use exponential notation to write repeated multiplication of the same quantity. For example, [latex]{2}^{4}[\/latex] means to multiply four factors of [latex]2[\/latex], so [latex]{2}^{4}[\/latex] means [latex]2\\cdot 2\\cdot 2\\cdot 2[\/latex].\u00a0 Conversely, [latex]10\\cdot10\\cdot10[\/latex] can be written more succinctly as [latex]10^{3}[\/latex]. The [latex]10[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>base<\/b>. The [latex]3[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>exponent<\/b>. The expression [latex]10^{3}[\/latex] is called the exponential expression. Knowing the names for the parts of an exponential expression or term will help you learn how to perform mathematical operations on them.<\/p>\n<div class=\"textbox shaded\">\n<h3>Exponential Notation<\/h3>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224353\/CNX_BMath_Figure_10_02_013_img.png\" alt=\"On the left side, a raised to the m is shown. The m is labeled in blue as an exponent. The a is labeled in red as the base. On the right, it says a to the m means multiply m factors of a. Below this, it says a to the m equals a times a times a times a, with m factors written below in blue.\" \/><br \/>\nThis is read [latex]a[\/latex] to the [latex]{m}^{\\mathrm{th}}[\/latex] power.<\/p>\n<\/div>\n<p>In the expression [latex]{a}^{m}[\/latex], the exponent tells us how many times we use the base [latex]a[\/latex] as a factor.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224355\/CNX_BMath_Figure_10_02_014_img.png\" alt=\"On the left side, 7 to the 3rd power is shown. Below is 7 times 7 times 7, with 3 factors written below. On the right side, parentheses negative 8 to the 5th power is shown. Below is negative 8 times negative 8 times negative 8 times negative 8 times negative 8, with 5 factors written below.\" \/><\/p>\n<p>[latex]10^{3}[\/latex] is read as \u201c[latex]10[\/latex] to the third power\u201d or \u201c[latex]10[\/latex] cubed.\u201d It means [latex]10\\cdot10\\cdot10[\/latex], or [latex]1,000[\/latex].<\/p>\n<p>[latex]8^{2}[\/latex]\u00a0is read as \u201c[latex]8[\/latex] to the second power\u201d or \u201c[latex]8[\/latex] squared.\u201d It means [latex]8\\cdot8[\/latex], or [latex]64[\/latex].<\/p>\n<p>[latex]5^{4}[\/latex]\u00a0is read as \u201c[latex]5[\/latex] to the fourth power.\u201d It means [latex]5\\cdot5\\cdot5\\cdot5[\/latex], or [latex]625[\/latex].<\/p>\n<p>[latex]b^{5}[\/latex]\u00a0is read as \u201cb to the fifth power.\u201d It means [latex]{b}\\cdot{b}\\cdot{b}\\cdot{b}\\cdot{b}[\/latex]. Its value will depend on the value of b.<\/p>\n<p>The exponent applies only to the number that it is next to. Therefore, in the expression [latex]xy^{4}[\/latex],\u00a0only the [latex]y[\/latex] is affected by the [latex]4[\/latex]. [latex]xy^{4}[\/latex]\u00a0means [latex]{x}\\cdot{y}\\cdot{y}\\cdot{y}\\cdot{y}[\/latex].<\/p>\n<p>If the exponential expression is negative, such as [latex]\u22123^{4}[\/latex], it means [latex]\u2013\\left(3\\cdot3\\cdot3\\cdot3\\right)[\/latex] or [latex]\u221281[\/latex].<\/p>\n<p>If [latex]\u22123[\/latex] is to be the base, it must be written as [latex]\\left(\u22123\\right)^{4}[\/latex], which means [latex]\u22123\\cdot\u22123\\cdot\u22123\\cdot\u22123[\/latex], or [latex]81[\/latex].<\/p>\n<p>Likewise,\u00a0[latex]\\left(\u2212x\\right)^{4}=\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)=x^{4}[\/latex], while [latex]\u2212x^{4}=\u2013\\left(x\\cdot x\\cdot x\\cdot x\\right)[\/latex].<\/p>\n<p>You can see that there is quite a difference, so you have to be very careful! The following examples show how to identify the base and the exponent, as well as how to identify the expanded and exponential format of writing repeated multiplication.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Identify the exponent and the base in the following terms, then simplify:<\/p>\n<ol>\n<li>[latex]7^{2}[\/latex]<\/li>\n<li>[latex]{\\left(\\frac{1}{2}\\right)}^{3}[\/latex]<\/li>\n<li>[latex]2x^{3}[\/latex]<\/li>\n<li>[latex]\\left(-5\\right)^{2}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q211363\">Show Solution<\/span><\/p>\n<p style=\"text-align: left;\">\n<div id=\"q211363\" class=\"hidden-answer\" style=\"display: none\">\n<p>1) [latex]7^{2}[\/latex]<\/p>\n<p>The exponent in this term is [latex]2[\/latex] and the base is [latex]7[\/latex]. To simplify, expand the term: [latex]7^{2}=7\\cdot{7}=49[\/latex]<\/p>\n<p>2) [latex]{\\left(\\frac{1}{2}\\right)}^{3}[\/latex]<\/p>\n<p>The exponent on this term is [latex]3[\/latex], and the base is [latex]\\frac{1}{2}[\/latex]. To simplify, expand the multiplication and remember how to multiply fractions: [latex]{\\left(\\frac{1}{2}\\right)}^{3}=\\frac{1}{2}\\cdot{\\frac{1}{2}}\\cdot{\\frac{1}{2}}=\\frac{1}{8}[\/latex]<\/p>\n<p>3) \u00a0[latex]2x^{3}[\/latex]<\/p>\n<p>The exponent on this term is [latex]3[\/latex], and the base is [latex]x[\/latex], the [latex]2[\/latex] is not getting the exponent because there are no parentheses that tell us it is. \u00a0This term is in its most simplified form.<\/p>\n<p>4)\u00a0[latex]\\left(-5\\right)^{2}[\/latex]<\/p>\n<p>The exponent on this terms is [latex]2[\/latex] and the base is [latex]-5[\/latex]. To simplify, expand the multiplication: [latex]\\left(-5\\right)^{2}=-5\\cdot{-5}=25[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p class=\"no-indent\">In the following video you are provided more examples of applying exponents to various bases.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Simplify  Basic Exponential Expressions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ocedY91LHKU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Before we begin working with variable expressions containing exponents, let\u2019s simplify a few expressions involving only numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]{5}^{3}[\/latex]<br \/>\n2. [latex]{9}^{1}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469452397\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{5}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply [latex]3[\/latex] factors of [latex]5[\/latex].<\/td>\n<td>[latex]5\\cdot 5\\cdot 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]125[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168046009892\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{9}^{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply [latex]1[\/latex] factor of [latex]9[\/latex].<\/td>\n<td>[latex]9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146094\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146094&theme=oea&iframe_resize_id=ohm146094&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]{\\left({\\Large\\frac{7}{8}}\\right)}^{2}[\/latex]<br \/>\n2. [latex]{\\left(0.74\\right)}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q153461\">Show Solution<\/span><\/p>\n<div id=\"q153461\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469451188\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\">1.<\/td>\n<td style=\"height: 15px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15.2334px;\">\n<td style=\"height: 15.2334px;\"><\/td>\n<td style=\"height: 15.2334px;\">[latex]{\\left({\\Large\\frac{7}{8}}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\">Multiply two factors.<\/td>\n<td style=\"height: 15px;\">[latex]\\left({\\Large\\frac{7}{8}}\\right)\\left({\\Large\\frac{7}{8}}\\right)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\">Simplify.<\/td>\n<td style=\"height: 15px;\">[latex]{\\Large\\frac{49}{64}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168047561610\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(0.74\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td>[latex]\\left(0.74\\right)\\left(0.74\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.5476[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146095\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146095&theme=oea&iframe_resize_id=ohm146095&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146867\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146867&theme=oea&iframe_resize_id=ohm146867&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]{\\left(-3\\right)}^{4}[\/latex]<br \/>\n2. [latex]{-3}^{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q152453\">Show Solution<\/span><\/p>\n<div id=\"q152453\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468562526\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(-3\\right)}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply four factors of [latex]\u22123[\/latex].<\/td>\n<td>[latex]\\left(-3\\right)\\left(-3\\right)\\left(-3\\right)\\left(-3\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]81[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168048408997\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{-3}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply two factors.<\/td>\n<td>[latex]-\\left(3\\cdot 3\\cdot 3\\cdot 3\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-81[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice the similarities and differences in parts 1 and 2. Why are the answers different? In part 1 the parentheses tell us to raise the [latex](\u22123)[\/latex] to the [latex]4[\/latex]<sup>th<\/sup> power. In part 2 we raise only the [latex]3[\/latex] to the [latex]4[\/latex]<sup>th<\/sup> power and then find the opposite.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146097\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146097&theme=oea&iframe_resize_id=ohm146097&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Evaluate expressions<\/h3>\n<p>Evaluating expressions containing exponents is the same as evaluating the linear expressions from earlier in the course. You substitute the value of the variable into the expression and simplify.<\/p>\n<p>You can use the order of operations\u00a0to evaluate the expressions containing exponents. First, evaluate anything in Parentheses or grouping symbols. Next, look for Exponents, followed by Multiplication and Division (reading from left to right), and lastly, Addition and Subtraction (again, reading from left to right).<\/p>\n<p>So, when you evaluate the expression [latex]5x^{3}[\/latex]\u00a0if [latex]x=4[\/latex], first substitute the value [latex]4[\/latex] for the variable [latex]x[\/latex]. Then evaluate, using order of operations.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate\u00a0[latex]5x^{3}[\/latex]\u00a0if [latex]x=4[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q411363\">Show Solution<\/span><\/p>\n<div id=\"q411363\" class=\"hidden-answer\" style=\"display: none\">\n<p>Substitute [latex]4[\/latex] for the variable [latex]x[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]5\\cdot4^{3}[\/latex]<\/p>\n<p>Evaluate [latex]4^{3}[\/latex]. Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]5\\left(4\\cdot4\\cdot4\\right)=5\\cdot64=320[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]5x^{3}=320[\/latex]\u00a0when [latex]x=4[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the example below, notice how adding parentheses can change the outcome when you are simplifying terms with exponents.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]\\left(5x\\right)^{3}[\/latex]\u00a0if [latex]x=4[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q362021\">Show Solution<\/span><\/p>\n<div id=\"q362021\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]4[\/latex] for the variable [latex]x[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\left(5\\cdot4\\right)3[\/latex]<\/p>\n<p>Multiply inside the parentheses, then apply the exponent\u2014following the rules of PEMDAS.<\/p>\n<p style=\"text-align: center;\">[latex]20^{3}[\/latex]<\/p>\n<p>Evaluate [latex]20^{3}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]20\\cdot20\\cdot20=8,000[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\left(5x\\right)3=8,000[\/latex] when [latex]x=4[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The addition of parentheses made quite a difference!\u00a0Parentheses allow you to apply an exponent to variables or numbers that are multiplied, divided, added, or subtracted to each other.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm53024\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=53024&theme=oea&iframe_resize_id=ohm53024&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]x^{3}[\/latex] if [latex]x=\u22124[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q86290\">Show Solution<\/span><\/p>\n<div id=\"q86290\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]\u22124[\/latex] for the variable x.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(\u22124\\right)^{3}[\/latex]<\/p>\n<p>Evaluate. Note how placing parentheses around the [latex]\u22124[\/latex] means the negative sign also gets multiplied.<\/p>\n<p style=\"text-align: center;\">[latex]\u22124\\cdot\u22124\\cdot\u22124[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\u22124\\cdot\u22124\\cdot\u22124=\u221264[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x^{3}=\u221264[\/latex] when [latex]x=\u22124[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2132 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/22011815\/traffic-sign-160659-300x265.png\" alt=\"Caution\" width=\"75\" height=\"66\" \/><\/p>\n<p>Caution! Whether to include a negative sign as part of a base or not often leads to confusion. To clarify\u00a0whether a negative sign is applied before or after the exponent, here is an example.<\/p>\n<p>&nbsp;<\/p>\n<p>What is the difference in the way you would evaluate these two terms?<\/p>\n<ol>\n<li style=\"text-align: left;\">[latex]-{3}^{2}[\/latex]<\/li>\n<li style=\"text-align: left;\">[latex]{\\left(-3\\right)}^{2}[\/latex]<\/li>\n<\/ol>\n<p>To evaluate 1), you would apply the exponent to the three first, then apply the negative sign last, like this:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}-\\left({3}^{2}\\right)\\\\=-\\left(9\\right) = -9\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left;\">To evaluate 2), you would apply the exponent to the [latex]3[\/latex] and the negative sign:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}{\\left(-3\\right)}^{2}\\\\=\\left(-3\\right)\\cdot\\left(-3\\right)\\\\={ 9}\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left;\">The key to remembering this is to follow the order of operations. The first expression does not include parentheses so you would apply the exponent to the integer [latex]3[\/latex] first, then apply the negative sign. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared.<\/p>\n<\/div>\n<p id=\"video0\" class=\"no-indent\" style=\"text-align: left;\">In the next sections, you will learn how to simplify expressions that contain exponents. Come back to this page if you forget how to apply the order of operations to a term with exponents, or forget which is the base and which is the exponent!<\/p>\n<p class=\"no-indent\" style=\"text-align: left;\">In the following video you are provided with examples of evaluating exponential expressions for a given number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Evaluate Basic Exponential Expressions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/pQNz8IpVVg0?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-16225\">\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>Simplify Basic Exponential Expressions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ocedY91LHKU\">https:\/\/youtu.be\/ocedY91LHKU<\/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>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>Screenshot: Repeated Image. <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 Basic Exponential Expressions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/pQNz8IpVVg0\">https:\/\/youtu.be\/pQNz8IpVVg0<\/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>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\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: 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