{"id":10829,"date":"2017-06-05T21:16:17","date_gmt":"2017-06-05T21:16:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10829"},"modified":"2017-08-09T21:21:53","modified_gmt":"2017-08-09T21:21:53","slug":"summary-simplifying-expressions-with-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-simplifying-expressions-with-exponents\/","title":{"raw":"Summary: Simplifying Expressions With Exponents","rendered":"Summary: Simplifying Expressions With Exponents"},"content":{"raw":"&nbsp;\r\n<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-277\">\r\n \t<li><strong>Exponential Notation<\/strong><\/li>\r\n<\/ul>\r\n<p style=\"padding-left: 150px;\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224415\/CNX_BMath_Figure_10_02_026_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.<\/p>\r\n\r\n<ul id=\"eip-277\">\r\n \t<li><strong>Product Property of Exponents<\/strong>\r\n<ul id=\"eip-id1170323937420\">\r\n \t<li>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then\r\n[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/li>\r\n \t<li>To multiply with like bases, add the exponents.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Power Property for Exponents<\/strong>\r\n<ul id=\"eip-id1170323046923\">\r\n \t<li>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then\r\n[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Product to a Power Property for Exponents<\/strong>\r\n<ul id=\"eip-id1170322772590\">\r\n \t<li>If [latex]a[\/latex] and [latex]b[\/latex] are real numbers and [latex]m[\/latex] is a whole number, then\r\n[latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2><\/h2>","rendered":"<p>&nbsp;<\/p>\n<h2>Key Concepts<\/h2>\n<ul id=\"eip-277\">\n<li><strong>Exponential Notation<\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 150px;\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224415\/CNX_BMath_Figure_10_02_026_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<ul id=\"eip-277\">\n<li><strong>Product Property of Exponents<\/strong>\n<ul id=\"eip-id1170323937420\">\n<li>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then<br \/>\n[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/li>\n<li>To multiply with like bases, add the exponents.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Power Property for Exponents<\/strong>\n<ul id=\"eip-id1170323046923\">\n<li>If [latex]a[\/latex] is a real number and [latex]m,n[\/latex] are counting numbers, then<br \/>\n[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Product to a Power Property for Exponents<\/strong>\n<ul id=\"eip-id1170322772590\">\n<li>If [latex]a[\/latex] and [latex]b[\/latex] are real numbers and [latex]m[\/latex] is a whole number, then<br \/>\n[latex]{\\left(ab\\right)}^{m}={a}^{m}{b}^{m}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2><\/h2>\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-10829\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><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":11,"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\"}]","CANDELA_OUTCOMES_GUID":"6188aa66-c163-485f-b16a-ae2eba9a7e4a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10829","chapter","type-chapter","status-publish","hentry"],"part":8336,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10829","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/21046"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10829\/revisions"}],"predecessor-version":[{"id":14123,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10829\/revisions\/14123"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/8336"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10829\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=10829"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10829"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=10829"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=10829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}