{"id":8381,"date":"2017-05-25T19:01:18","date_gmt":"2017-05-25T19:01:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=8381"},"modified":"2021-05-21T21:24:54","modified_gmt":"2021-05-21T21:24:54","slug":"use-multiplication-properties-of-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/use-multiplication-properties-of-exponents\/","title":{"raw":"Introduction to Applying Exponent Rules","rendered":"Introduction to Applying Exponent Rules"},"content":{"raw":"<h2>What you'll learn to do: Simplify expressions using properties of exponents<\/h2>\r\nIn this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents. We will also learn how to use scientific notation to represent very large or very small numbers, and perform mathematical operations on them.\r\n\r\nSpecifically, in this section you\u2019ll learn how to:\r\n<ul>\r\n \t<li>Evaluate exponential expressions<\/li>\r\n \t<li>Simplify expressions using the Product Property of Exponents<\/li>\r\n \t<li>Simplify expressions using the Power Rule of Exponents<\/li>\r\n \t<li>Simplify expressions using the Product to a Power Property<\/li>\r\n \t<li>Simplify expressions using the Quotient Properties of Exponents<\/li>\r\n \t<li>Simplify exponential expressions containing negative exponents and exponents of 0 and 1<\/li>\r\n \t<li>Simplify complex expressions using a combination of exponent rules<\/li>\r\n \t<li>Simplify compound expressions using a combination of exponent rules<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\nBefore you get started, take this readiness quiz.\r\n<div class=\"textbox examples\">\r\n<h3>Readiness Quiz<\/h3>\r\n1)\r\n\r\n[ohm_question]144737[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/HkPGTmAmg_s\r\n\r\n2)\r\n\r\n[ohm_question]144745[\/ohm_question]\r\n\r\nIf you missed the problem, review the example below.\r\n<div class=\"textbox shaded\">Simplify: [latex]{3}^{4}[\/latex][reveal-answer q=\"534998\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"534998\"]Solution\r\n<table id=\"eip-id1164752752096\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{3}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Expand the expression.<\/td>\r\n<td>[latex]3\\cdot 3\\cdot 3\\cdot 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply left to right.<\/td>\r\n<td>[latex]9\\cdot 3\\cdot 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]27\\cdot 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]81[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n3)\r\n\r\n[ohm_question]145337[\/ohm_question]\r\n\r\nIf you missed the problem, review this video.\r\n\r\nhttps:\/\/youtu.be\/qB5PZzmjenI\r\n\r\n4)\r\n\r\n[ohm_question]130[\/ohm_question]\r\n\r\nIf you missed this problem, review this video.\r\n\r\nhttps:\/\/youtu.be\/0-4rLGvVEOI\r\n\r\n5)\r\n\r\n[ohm_question]146568[\/ohm_question]\r\n\r\nIf you missed this problem, review the video below.\r\n\r\nhttps:\/\/youtu.be\/aLsWWl2-aNE\r\n\r\n6)\r\n\r\n[ohm_question]145195[\/ohm_question]\r\n\r\nIf you missed this problem, review the following example.\r\n<div class=\"textbox shaded\">\r\n\r\nSimplify:\r\n\r\n[latex]-7-\\left(-4\\right)\\text{ and }-7+4[\/latex]\r\n\r\n[reveal-answer q=\"433827\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"433827\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1164270694692\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-7-\\left(-4\\right)[\/latex] and [latex]-7+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract to simplify.<\/td>\r\n<td>[latex]-7-\\left(-4\\right)=-3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add to simplify.<\/td>\r\n<td>[latex]-7+4=-3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtracting [latex]\u22124[\/latex] from [latex]\u22127[\/latex] is the same as adding [latex]4[\/latex] to [latex]\u22127[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1gLnfo4OtADtaA9s63jBj1P3q7N6aMmhzZFxFLO8iQL8\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Simplify expressions using properties of exponents<\/h2>\n<p>In this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents. We will also learn how to use scientific notation to represent very large or very small numbers, and perform mathematical operations on them.<\/p>\n<p>Specifically, in this section you\u2019ll learn how to:<\/p>\n<ul>\n<li>Evaluate exponential expressions<\/li>\n<li>Simplify expressions using the Product Property of Exponents<\/li>\n<li>Simplify expressions using the Power Rule of Exponents<\/li>\n<li>Simplify expressions using the Product to a Power Property<\/li>\n<li>Simplify expressions using the Quotient Properties of Exponents<\/li>\n<li>Simplify exponential expressions containing negative exponents and exponents of 0 and 1<\/li>\n<li>Simplify complex expressions using a combination of exponent rules<\/li>\n<li>Simplify compound expressions using a combination of exponent rules<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>Before you get started, take this readiness quiz.<\/p>\n<div class=\"textbox examples\">\n<h3>Readiness Quiz<\/h3>\n<p>1)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144737\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144737&theme=oea&iframe_resize_id=ohm144737&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example:  Write Repeated Multiplication in Exponential Form\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/HkPGTmAmg_s?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>2)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144745\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144745&theme=oea&iframe_resize_id=ohm144745&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed the problem, review the example below.<\/p>\n<div class=\"textbox shaded\">Simplify: [latex]{3}^{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q534998\">Show Solution<\/span><\/p>\n<div id=\"q534998\" class=\"hidden-answer\" style=\"display: none\">Solution<\/p>\n<table id=\"eip-id1164752752096\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{3}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Expand the expression.<\/td>\n<td>[latex]3\\cdot 3\\cdot 3\\cdot 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply left to right.<\/td>\n<td>[latex]9\\cdot 3\\cdot 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]27\\cdot 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]81[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>3)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm145337\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145337&theme=oea&iframe_resize_id=ohm145337&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed the problem, review this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Evaluating Negative Numbers Raised to Powers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qB5PZzmjenI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>4)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm130\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=130&theme=oea&iframe_resize_id=ohm130&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Examples:  Determining Place Value\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0-4rLGvVEOI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>5)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146568\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146568&theme=oea&iframe_resize_id=ohm146568&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the video below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Read and Write Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aLsWWl2-aNE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>6)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm145195\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145195&theme=oea&iframe_resize_id=ohm145195&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the following example.<\/p>\n<div class=\"textbox shaded\">\n<p>Simplify:<\/p>\n<p>[latex]-7-\\left(-4\\right)\\text{ and }-7+4[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q433827\">Show Solution<\/span><\/p>\n<div id=\"q433827\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1164270694692\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-7-\\left(-4\\right)[\/latex] and [latex]-7+4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract to simplify.<\/td>\n<td>[latex]-7-\\left(-4\\right)=-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add to simplify.<\/td>\n<td>[latex]-7+4=-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtracting [latex]\u22124[\/latex] from [latex]\u22127[\/latex] is the same as adding [latex]4[\/latex] to [latex]\u22127[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1gLnfo4OtADtaA9s63jBj1P3q7N6aMmhzZFxFLO8iQL8\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/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-8381\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Evaluating Negative Numbers Raised to Powers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/qB5PZzmjenI\">https:\/\/youtu.be\/qB5PZzmjenI<\/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> Example: Write Repeated Multiplication in Exponential Form. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/HkPGTmAmg_s\">https:\/\/youtu.be\/HkPGTmAmg_s<\/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>Question ID: 144737, 144745, 145337. <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>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/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":21,"menu_order":26,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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