{"id":10827,"date":"2017-06-05T21:15:52","date_gmt":"2017-06-05T21:15:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10827"},"modified":"2017-09-23T23:11:31","modified_gmt":"2017-09-23T23:11:31","slug":"simplifying-variable-expressions-using-exponent-properties","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/simplifying-variable-expressions-using-exponent-properties\/","title":{"raw":"Simplifying Variable Expressions Using Exponent Properties","rendered":"Simplifying Variable Expressions Using Exponent Properties"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the product property of exponents to simplify expressions<\/li>\r\n \t<li>Use the power property of exponents to simplify expressions<\/li>\r\n \t<li>Use the product to a power property of exponents to simplify expressions<\/li>\r\n<\/ul>\r\n<\/div>\r\nYou have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. We\u2019ll derive the properties of exponents by looking for patterns in several examples. All the exponent properties hold true for any real numbers, but right now we will only use whole number exponents.\r\n\r\nFirst, we will look at an example that leads to the Product Property.\r\n<table id=\"eip-id1168468520971\" class=\"unnumbered unstyled\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{x}^{2}\\cdot{x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What does this mean?\r\n\r\nHow many factors altogether?<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224357\/CNX_BMath_Figure_10_02_015_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, we have<\/td>\r\n<td>[latex]{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}={x}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that [latex]5[\/latex] is the sum of the exponents, [latex]2[\/latex] and [latex]3[\/latex].<\/td>\r\n<td>[latex]{x}^{2}\\cdot{x}^{3}[\/latex] is [latex]{x}^{2+3}[\/latex], or [latex]{x}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We write:<\/td>\r\n<td>[latex]{x}^{2}\\cdot {x}^{3}[\/latex]\r\n\r\n[latex]{x}^{2+3}[\/latex]\r\n\r\n[latex]{x}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe base stayed the same and we added the exponents. This leads to the Product Property for Exponents.\r\n<div class=\"textbox shaded\">\r\n<h3>Product Property of Exponents<\/h3>\r\nIf [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then\r\n\r\n[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]\r\nTo multiply with like bases, add the exponents.\r\n\r\n<\/div>\r\nAn example with numbers helps to verify this property.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {2}^{2}\\cdot {2}^{3}&amp; \\stackrel{?}{=}&amp; {2}^{2+3}\\hfill \\\\ \\hfill 4\\cdot 8&amp; \\stackrel{?}{=}&amp; {2}^{5}\\hfill \\\\ \\hfill 32&amp; =&amp; 32\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{x}^{5}\\cdot {x}^{7}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168466105371\" class=\"unnumbered unstyled\" summary=\"The top line says x to the 5th times x to the 7th. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{x}^{5}\\cdot {x}^{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\r\n<td>[latex]x^{\\color{red}{5+7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{x}^{12}[\/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]146102[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{b}^{4}\\cdot b[\/latex]\r\n[reveal-answer q=\"338898\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"338898\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466637014\" class=\"unnumbered unstyled\" summary=\"The top line says b to the 4th times b. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{b}^{4}\\cdot b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite, [latex]b={b}^{1}[\/latex].<\/td>\r\n<td>[latex]{b}^{4}\\cdot {b}^{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\r\n<td>[latex]b^{\\color{red}{4+1}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{b}^{5}[\/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]146107[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{2}^{7}\\cdot {2}^{9}[\/latex]\r\n[reveal-answer q=\"971008\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"971008\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469803212\" class=\"unnumbered unstyled\" summary=\"The top line says 2 to the 7th times 2 to the 9th. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{2}^{7}\\cdot {2}^{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\r\n<td>[latex]2^{\\color{red}{7+9}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{2}^{16}[\/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]146143[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{y}^{17}\\cdot {y}^{23}[\/latex]\r\n[reveal-answer q=\"366560\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"366560\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469684383\" class=\"unnumbered unstyled\" summary=\"The top line shows y to the 17 times y to the 23rd. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{y}^{17}\\cdot {y}^{23}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice, the bases are the same, so add the exponents.<\/td>\r\n<td>[latex]y^{\\color{red}{17+23}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{y}^{40}[\/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]146144[\/ohm_question]\r\n\r\n<\/div>\r\nWe can extend the Product Property of Exponents to more than two factors.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{x}^{3}\\cdot {x}^{4}\\cdot {x}^{2}[\/latex]\r\n[reveal-answer q=\"278257\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"278257\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468510734\" class=\"unnumbered unstyled\" summary=\"The top line shows x to the 3rd times x to the 4th times x squared. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{x}^{3}\\cdot {x}^{4}\\cdot {x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the exponents, since the bases are the same.<\/td>\r\n<td>[latex]x^{\\color{red}{3+4+2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{x}^{9}[\/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]146145[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to use the product rule for exponents to simplify expressions.\r\n\r\nhttps:\/\/youtu.be\/P0UVIMy2nuI\r\n<h3>Simplify Expressions Using the Power Property of Exponents<\/h3>\r\nNow let\u2019s look at an exponential expression that contains a power raised to a power. See if you can discover a general property.\r\n<table id=\"eip-id1168466113470\" class=\"unnumbered unstyled\" summary=\"The top line shows x squared in parentheses raised to the third power. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]({x}^{2})^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{x}^{2}\\cdot{x}^{2}\\cdot{x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What does this mean?\r\n\r\nHow many factors altogether?<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224409\/CNX_BMath_Figure_10_02_021_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, we have<\/td>\r\n<td>[latex]{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}={x}^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that [latex]6[\/latex] is the product of the exponents, [latex]2[\/latex] and [latex]3[\/latex].<\/td>\r\n<td>[latex]({x}^{2})^{3}[\/latex] is [latex]{x}^{2\\cdot3}[\/latex] or [latex]{x}^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We write:<\/td>\r\n<td>[latex]{\\left({x}^{2}\\right)}^{3}[\/latex]\r\n\r\n[latex]{x}^{2\\cdot 3}[\/latex]\r\n\r\n[latex]{x}^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe multiplied the exponents. This leads to the Power Property for Exponents.\r\n<div class=\"textbox shaded\">\r\n<h3>Power Property of Exponents<\/h3>\r\nIf [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are whole numbers, then\r\n\r\n[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]\r\nTo raise a power to a power, multiply the exponents.\r\n\r\n<\/div>\r\nAn example with numbers helps to verify this property.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {\\left({5}^{2}\\right)}^{3}&amp; \\stackrel{?}{=}&amp; {5}^{2\\cdot 3}\\hfill \\\\ \\hfill {\\left(25\\right)}^{3}&amp; \\stackrel{?}{=}&amp; {5}^{6}\\hfill \\\\ \\hfill 15,625&amp; =&amp; 15,625\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n\r\n1. [latex]{\\left({x}^{5}\\right)}^{7}[\/latex]\r\n2. [latex]{\\left({3}^{6}\\right)}^{8}[\/latex]\r\n[reveal-answer q=\"411160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"411160\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468674718\" class=\"unnumbered unstyled\" summary=\"The top line shows x to the 5th in parentheses raised to the 7th. The next line says, \">\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({x}^{5}\\right)}^{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\r\n<td>[latex]x^{\\color{red}{5\\cdot{7}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{x}^{35}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168047388004\" class=\"unnumbered unstyled\" summary=\"The top line shows 3 to the 6th in parentheses raised to the 8th power. The next line says, \">\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({3}^{6}\\right)}^{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\r\n<td>[latex]3^{\\color{red}{6\\cdot{8}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{3}^{48}[\/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]146148[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples of how to use the power rule for exponents to simplify expressions.\r\n\r\nhttps:\/\/youtu.be\/Hgu9HKDHTUA\r\n<h3>Simplify Expressions Using the Product to a Power Property<\/h3>\r\nWe will now look at an expression containing a product that is raised to a power. Look for a pattern.\r\n<table id=\"eip-id1168468541414\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(2x\\right)}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What does this mean?<\/td>\r\n<td>[latex]2x\\cdot 2x\\cdot 2x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We group the like factors together.<\/td>\r\n<td>[latex]2\\cdot 2\\cdot 2\\cdot x\\cdot x\\cdot x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>How many factors of [latex]2[\/latex] and of [latex]x?[\/latex]<\/td>\r\n<td>[latex]{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that each factor was raised to the power.<\/td>\r\n<td>[latex]{\\left(2x\\right)}^{3}\\text{ is }{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We write:<\/td>\r\n<td>[latex]{\\left(2x\\right)}^{3}[\/latex]\r\n\r\n[latex]{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe exponent applies to each of the factors. This leads to the Product to a Power Property for Exponents.\r\n<div class=\"textbox shaded\">\r\n<h3>Product to a Power Property of Exponents<\/h3>\r\nIf [latex]a[\/latex] and [latex]b[\/latex] are real numbers and [latex]m[\/latex] is a whole number, then\r\n\r\n[latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex]\r\nTo raise a product to a power, raise each factor to that power.\r\n\r\n<\/div>\r\nAn example with numbers helps to verify this property:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {\\left(2\\cdot 3\\right)}^{2}&amp; \\stackrel{?}{=}&amp; {2}^{2}\\cdot {3}^{2}\\hfill \\\\ \\hfill {6}^{2}&amp; \\stackrel{?}{=}&amp; 4\\cdot 9\\hfill \\\\ \\hfill 36&amp; =&amp; 36\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left(-11x\\right)}^{2}[\/latex]\r\n[reveal-answer q=\"390160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"390160\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466596049\" class=\"unnumbered unstyled\" summary=\"The top line shows negative 11x in parentheses, squared. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(-11x\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power of a Product Property, [latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex].<\/td>\r\n<td>[latex](-11)^{\\color{red}{2}}x^{\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]121{x}^{2}[\/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]146152[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left(3xy\\right)}^{3}[\/latex]\r\n[reveal-answer q=\"678819\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"678819\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466034982\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 3xy to the third. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(3xy\\right)}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Raise each factor to the third power.<\/td>\r\n<td>[latex]3^{\\color{red}{3}}x^{\\color{red}{3}}y^{\\color{red}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]27{x}^{3}{y}^{3}[\/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]146154[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show more examples of how to simplify a product raised to a power.\r\n\r\nhttps:\/\/youtu.be\/D05D-YIPr1Q","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the product property of exponents to simplify expressions<\/li>\n<li>Use the power property of exponents to simplify expressions<\/li>\n<li>Use the product to a power property of exponents to simplify expressions<\/li>\n<\/ul>\n<\/div>\n<p>You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. We\u2019ll derive the properties of exponents by looking for patterns in several examples. All the exponent properties hold true for any real numbers, but right now we will only use whole number exponents.<\/p>\n<p>First, we will look at an example that leads to the Product Property.<\/p>\n<table id=\"eip-id1168468520971\" class=\"unnumbered unstyled\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{x}^{2}\\cdot{x}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>What does this mean?<\/p>\n<p>How many factors altogether?<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224357\/CNX_BMath_Figure_10_02_015_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>So, we have<\/td>\n<td>[latex]{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}={x}^{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Notice that [latex]5[\/latex] is the sum of the exponents, [latex]2[\/latex] and [latex]3[\/latex].<\/td>\n<td>[latex]{x}^{2}\\cdot{x}^{3}[\/latex] is [latex]{x}^{2+3}[\/latex], or [latex]{x}^{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We write:<\/td>\n<td>[latex]{x}^{2}\\cdot {x}^{3}[\/latex]<\/p>\n<p>[latex]{x}^{2+3}[\/latex]<\/p>\n<p>[latex]{x}^{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The base stayed the same and we added the exponents. This leads to the Product Property for Exponents.<\/p>\n<div class=\"textbox shaded\">\n<h3>Product Property of Exponents<\/h3>\n<p>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then<\/p>\n<p>[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<br \/>\nTo multiply with like bases, add the exponents.<\/p>\n<\/div>\n<p>An example with numbers helps to verify this property.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {2}^{2}\\cdot {2}^{3}& \\stackrel{?}{=}& {2}^{2+3}\\hfill \\\\ \\hfill 4\\cdot 8& \\stackrel{?}{=}& {2}^{5}\\hfill \\\\ \\hfill 32& =& 32\\hfill \\end{array}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{x}^{5}\\cdot {x}^{7}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466105371\" class=\"unnumbered unstyled\" summary=\"The top line says x to the 5th times x to the 7th. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{x}^{5}\\cdot {x}^{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\n<td>[latex]x^{\\color{red}{5+7}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{x}^{12}[\/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=\"ohm146102\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146102&theme=oea&iframe_resize_id=ohm146102&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: [latex]{b}^{4}\\cdot b[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q338898\">Show Solution<\/span><\/p>\n<div id=\"q338898\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466637014\" class=\"unnumbered unstyled\" summary=\"The top line says b to the 4th times b. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{b}^{4}\\cdot b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite, [latex]b={b}^{1}[\/latex].<\/td>\n<td>[latex]{b}^{4}\\cdot {b}^{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\n<td>[latex]b^{\\color{red}{4+1}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{b}^{5}[\/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=\"ohm146107\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146107&theme=oea&iframe_resize_id=ohm146107&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: [latex]{2}^{7}\\cdot {2}^{9}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q971008\">Show Solution<\/span><\/p>\n<div id=\"q971008\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469803212\" class=\"unnumbered unstyled\" summary=\"The top line says 2 to the 7th times 2 to the 9th. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{2}^{7}\\cdot {2}^{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the product property, [latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex].<\/td>\n<td>[latex]2^{\\color{red}{7+9}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{2}^{16}[\/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=\"ohm146143\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146143&theme=oea&iframe_resize_id=ohm146143&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: [latex]{y}^{17}\\cdot {y}^{23}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q366560\">Show Solution<\/span><\/p>\n<div id=\"q366560\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469684383\" class=\"unnumbered unstyled\" summary=\"The top line shows y to the 17 times y to the 23rd. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{y}^{17}\\cdot {y}^{23}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Notice, the bases are the same, so add the exponents.<\/td>\n<td>[latex]y^{\\color{red}{17+23}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{y}^{40}[\/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=\"ohm146144\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146144&theme=oea&iframe_resize_id=ohm146144&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>We can extend the Product Property of Exponents to more than two factors.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{x}^{3}\\cdot {x}^{4}\\cdot {x}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q278257\">Show Solution<\/span><\/p>\n<div id=\"q278257\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468510734\" class=\"unnumbered unstyled\" summary=\"The top line shows x to the 3rd times x to the 4th times x squared. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{x}^{3}\\cdot {x}^{4}\\cdot {x}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents, since the bases are the same.<\/td>\n<td>[latex]x^{\\color{red}{3+4+2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{x}^{9}[\/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=\"ohm146145\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146145&theme=oea&iframe_resize_id=ohm146145&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to use the product rule for exponents to simplify expressions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Simplify Expressions Using the Product Rule of Exponents (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P0UVIMy2nuI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Simplify Expressions Using the Power Property of Exponents<\/h3>\n<p>Now let\u2019s look at an exponential expression that contains a power raised to a power. See if you can discover a general property.<\/p>\n<table id=\"eip-id1168466113470\" class=\"unnumbered unstyled\" summary=\"The top line shows x squared in parentheses raised to the third power. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]({x}^{2})^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{x}^{2}\\cdot{x}^{2}\\cdot{x}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>What does this mean?<\/p>\n<p>How many factors altogether?<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224409\/CNX_BMath_Figure_10_02_021_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>So, we have<\/td>\n<td>[latex]{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}={x}^{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Notice that [latex]6[\/latex] is the product of the exponents, [latex]2[\/latex] and [latex]3[\/latex].<\/td>\n<td>[latex]({x}^{2})^{3}[\/latex] is [latex]{x}^{2\\cdot3}[\/latex] or [latex]{x}^{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We write:<\/td>\n<td>[latex]{\\left({x}^{2}\\right)}^{3}[\/latex]<\/p>\n<p>[latex]{x}^{2\\cdot 3}[\/latex]<\/p>\n<p>[latex]{x}^{6}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We multiplied the exponents. This leads to the Power Property for Exponents.<\/p>\n<div class=\"textbox shaded\">\n<h3>Power Property of Exponents<\/h3>\n<p>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are whole numbers, then<\/p>\n<p>[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<br \/>\nTo raise a power to a power, multiply the exponents.<\/p>\n<\/div>\n<p>An example with numbers helps to verify this property.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {\\left({5}^{2}\\right)}^{3}& \\stackrel{?}{=}& {5}^{2\\cdot 3}\\hfill \\\\ \\hfill {\\left(25\\right)}^{3}& \\stackrel{?}{=}& {5}^{6}\\hfill \\\\ \\hfill 15,625& =& 15,625\\hfill \\end{array}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<p>1. [latex]{\\left({x}^{5}\\right)}^{7}[\/latex]<br \/>\n2. [latex]{\\left({3}^{6}\\right)}^{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q411160\">Show Solution<\/span><\/p>\n<div id=\"q411160\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468674718\" class=\"unnumbered unstyled\" summary=\"The top line shows x to the 5th in parentheses raised to the 7th. The next line says,\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\left({x}^{5}\\right)}^{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\n<td>[latex]x^{\\color{red}{5\\cdot{7}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{x}^{35}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168047388004\" class=\"unnumbered unstyled\" summary=\"The top line shows 3 to the 6th in parentheses raised to the 8th power. The next line says,\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\left({3}^{6}\\right)}^{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\n<td>[latex]3^{\\color{red}{6\\cdot{8}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{3}^{48}[\/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=\"ohm146148\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146148&theme=oea&iframe_resize_id=ohm146148&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples of how to use the power rule for exponents to simplify expressions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Simplify Exponential Expressions Using the Power Property of Exponents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Hgu9HKDHTUA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Simplify Expressions Using the Product to a Power Property<\/h3>\n<p>We will now look at an expression containing a product that is raised to a power. Look for a pattern.<\/p>\n<table id=\"eip-id1168468541414\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(2x\\right)}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>What does this mean?<\/td>\n<td>[latex]2x\\cdot 2x\\cdot 2x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We group the like factors together.<\/td>\n<td>[latex]2\\cdot 2\\cdot 2\\cdot x\\cdot x\\cdot x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>How many factors of [latex]2[\/latex] and of [latex]x?[\/latex]<\/td>\n<td>[latex]{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Notice that each factor was raised to the power.<\/td>\n<td>[latex]{\\left(2x\\right)}^{3}\\text{ is }{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We write:<\/td>\n<td>[latex]{\\left(2x\\right)}^{3}[\/latex]<\/p>\n<p>[latex]{2}^{3}\\cdot {x}^{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The exponent applies to each of the factors. This leads to the Product to a Power Property for Exponents.<\/p>\n<div class=\"textbox shaded\">\n<h3>Product to a Power Property of Exponents<\/h3>\n<p>If [latex]a[\/latex] and [latex]b[\/latex] are real numbers and [latex]m[\/latex] is a whole number, then<\/p>\n<p>[latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex]<br \/>\nTo raise a product to a power, raise each factor to that power.<\/p>\n<\/div>\n<p>An example with numbers helps to verify this property:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {\\left(2\\cdot 3\\right)}^{2}& \\stackrel{?}{=}& {2}^{2}\\cdot {3}^{2}\\hfill \\\\ \\hfill {6}^{2}& \\stackrel{?}{=}& 4\\cdot 9\\hfill \\\\ \\hfill 36& =& 36\\hfill \\end{array}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\left(-11x\\right)}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q390160\">Show Solution<\/span><\/p>\n<div id=\"q390160\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466596049\" class=\"unnumbered unstyled\" summary=\"The top line shows negative 11x in parentheses, squared. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(-11x\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power of a Product Property, [latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex].<\/td>\n<td>[latex](-11)^{\\color{red}{2}}x^{\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]121{x}^{2}[\/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=\"ohm146152\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146152&theme=oea&iframe_resize_id=ohm146152&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: [latex]{\\left(3xy\\right)}^{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q678819\">Show Solution<\/span><\/p>\n<div id=\"q678819\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466034982\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 3xy to the third. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(3xy\\right)}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Raise each factor to the third power.<\/td>\n<td>[latex]3^{\\color{red}{3}}x^{\\color{red}{3}}y^{\\color{red}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]27{x}^{3}{y}^{3}[\/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=\"ohm146154\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146154&theme=oea&iframe_resize_id=ohm146154&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show more examples of how to simplify a product raised to a power.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex: Simplify Exponential Expressions Using Power Property - Products to Powers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/D05D-YIPr1Q?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-10827\">\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>Question ID 146154, 146153, 146152. <strong>Authored 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>Ex: Simplify Exponential Expressions Using the Power Property of Exponents. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Hgu9HKDHTUA\">https:\/\/youtu.be\/Hgu9HKDHTUA<\/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>Simplify Expressions Using the Product Rule of Exponents (Basic). <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/P0UVIMy2nuI\">https:\/\/youtu.be\/P0UVIMy2nuI<\/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: Simplify Exponential Expressions Using Power Property - Products to Powers. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/D05D-YIPr1Q\">https:\/\/youtu.be\/D05D-YIPr1Q<\/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, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":21046,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146154, 146153, 146152\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Simplify Expressions Using the Product Rule of Exponents (Basic)\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/P0UVIMy2nuI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Ex: Simplify Exponential Expressions Using the Power Property of Exponents\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Hgu9HKDHTUA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Simplify Exponential Expressions Using Power Property - 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