{"id":154,"date":"2022-04-13T10:10:50","date_gmt":"2022-04-13T10:10:50","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=154"},"modified":"2025-01-18T06:47:48","modified_gmt":"2025-01-18T06:47:48","slug":"h-7-powers-of-monomials","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/h-7-powers-of-monomials\/","title":{"rendered":"H.7 Powers of monomials"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong> Powers of monomials<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-04d9d6410ea0aa79bd5fd62d138d8458\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Definition:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A <strong>monomial<\/strong> is an algebraic expression consisting of a single term.<\/li>\n\n\n\n<li class=\"has-large-font-size\">The <strong>power of a monomial<\/strong> is determined by the exponent of the variable in that term.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">General Form:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A monomial in the form \ufffd\ufffd\ufffd<em>a<\/em><em>x<\/em><em>n<\/em>, where \ufffd<em>a<\/em> is the coefficient, \ufffd<em>x<\/em> is the variable, and \ufffd<em>n<\/em> is the exponent.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Rules for Multiplying Monomials:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Product of Coefficients:<\/strong> \ufffd\u22c5\ufffd=\ufffd\ufffd<em>a<\/em>\u22c5<em>b<\/em>=<em>ab<\/em><\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Product of Variables:<\/strong> \ufffd\ufffd\u22c5\ufffd\ufffd=\ufffd\ufffd+\ufffd<em>x<\/em><em>n<\/em>\u22c5<em>x<\/em><em>m<\/em>=<em>x<\/em><em>n<\/em>+<em>m<\/em><\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Product of Powers with the Same Base:<\/strong> (\ufffd\ufffd)\ufffd=\ufffd\ufffd\ufffd(<em>x<\/em><em>n<\/em>)<em>m<\/em>=<em>x<\/em><em>nm<\/em><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Rules for Dividing Monomials:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Quotient of Coefficients:<\/strong> \ufffd\ufffd=\ufffd\ufffd<em>b<\/em><em>a<\/em>\u200b=<em>b<\/em><em>a<\/em>\u200b<\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Quotient of Variables:<\/strong> \ufffd\ufffd\ufffd\ufffd=\ufffd\ufffd\u2212\ufffd<em>x<\/em><em>m<\/em><em>x<\/em><em>n<\/em>\u200b=<em>x<\/em><em>n<\/em>\u2212<em>m<\/em><\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Quotient of Powers with the Same Base:<\/strong> \ufffd\ufffd\ufffd\ufffd=\ufffd\ufffd\u2212\ufffd<em>x<\/em><em>m<\/em><em>x<\/em><em>n<\/em>\u200b=<em>x<\/em><em>n<\/em>\u2212<em>m<\/em><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Power of a Monomial Raised to a Power:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">(\ufffd\ufffd\ufffd)\ufffd=\ufffd\ufffd\u22c5\ufffd\ufffd\ufffd(<em>a<\/em><em>x<\/em><em>n<\/em>)<em>m<\/em>=<em>a<\/em><em>m<\/em>\u22c5<em>x<\/em><em>nm<\/em><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Zero Exponent:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">\ufffd0=1<em>x<\/em>0=1 for any nonzero value of \ufffd<em>x<\/em>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Negative Exponent:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">\ufffd\u2212\ufffd=1\ufffd\ufffd<em>x<\/em>\u2212<em>n<\/em>=<em>x<\/em><em>n<\/em>1\u200b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Examples:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\">2\ufffd3\u22c53\ufffd2=6\ufffd52<em>x<\/em>3\u22c53<em>x<\/em>2=6<em>x<\/em>5<\/li>\n\n\n\n<li class=\"has-large-font-size\">4\ufffd42\ufffd2=2\ufffd22<em>x<\/em>24<em>x<\/em>4\u200b=2<em>x<\/em>2<\/li>\n\n\n\n<li class=\"has-large-font-size\">(2\ufffd3)2=4\ufffd6(2<em>x<\/em>3)2=4<em>x<\/em>6<\/li>\n\n\n\n<li class=\"has-large-font-size\">5\ufffd3\u22c55\ufffd\u22122=25\ufffd5<em>x<\/em>3\u22c55<em>x<\/em>\u22122=25<em>x<\/em><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Practice Tips:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Be careful with signs when multiplying or dividing monomials.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Understand the role of exponents in combining monomials.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Practice simplifying expressions involving the powers of monomials.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b1f4dc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u27a1\ufe0f Simplify.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aad60d81a3b12c118d81712b2df833ac\" style=\"color:#b00012\">Express your answer using a single&nbsp;exponent.<\/p>\n\n\n\n<p>(10r<sup>4<\/sup>)<sup>4<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;10r<sup>4<\/sup><sub>&nbsp;<sup>i<\/sup><\/sub>s raised to the power of&nbsp;4.&nbsp;First, raise each factor to the power of&nbsp;4.&nbsp;Then, multiply the&nbsp;exponents.<\/p>\n\n\n\n<p>(10<sup>r4<\/sup>)<sup>4<\/sup>=10<sup><strong>4<\/strong>(<\/sup>r<sup>4<\/sup>)<strong><sup>4<\/sup><\/strong>               Raise&nbsp;each factor to the power of&nbsp;4<\/p>\n\n\n\n<p>=<strong>10000<\/strong>(r<sup>4<\/sup>)<sup>4    <\/sup>              Simplify<\/p>\n\n\n\n<p>=10000r<sup>(<strong>4 . 4<\/strong>)  <\/sup>            Simplify&nbsp;(r<sup>4<\/sup>)<sup>4<\/sup>,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p>=10000r<sup><strong>16<\/strong>   <\/sup>             Multiply<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ffdaef\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u27a1\ufe0f Simplify.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aad60d81a3b12c118d81712b2df833ac\" style=\"color:#b00012\">Express your answer using a single&nbsp;exponent.<\/p>\n\n\n\n<p>(4a<sup>9<\/sup>)<sup>4<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;4a<sup>9&nbsp;<\/sup>is raised to the power of&nbsp;4.&nbsp;First, raise each factor to the power of&nbsp;4.&nbsp;Then, multiply the&nbsp;exponents.<\/p>\n\n\n\n<p>(4a<sup>9<\/sup>)<sup>4<\/sup>=4<strong><sup>4<\/sup><\/strong>(a<sup>9<\/sup>)<sup><strong>4<\/strong> <\/sup>                  Raise&nbsp;each factor to the power of&nbsp;4<\/p>\n\n\n\n<p>=<strong>256<\/strong>(a<sup>9<\/sup>)<sup>4<\/sup>                      Simplify<\/p>\n\n\n\n<p>=256a<sup>(<strong>9 . 4<\/strong>)     <\/sup>            Simplify&nbsp;(a<sup>9<\/sup>)<sup>4<\/sup>,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n\n\n\n<p>=256a<strong><sup>36<\/sup><\/strong>                Multiply<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d9f6d3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u27a1\ufe0f Simplify.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aad60d81a3b12c118d81712b2df833ac\" style=\"color:#b00012\">Express your answer using a single&nbsp;exponent.<\/p>\n\n\n\n<p>(6p<sup>6<\/sup>)<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;6p<sup>6&nbsp;<\/sup>is raised to the power of&nbsp;2.&nbsp;First, raise each factor to the power of&nbsp;2.&nbsp;Then, multiply the&nbsp;exponents.<\/p>\n\n\n\n<p>(6p<sup>6<\/sup>)<sup>2<\/sup>=6<strong><sup>2<\/sup><\/strong>(p<sup>6<\/sup>)<sup><strong>2<\/strong>  <\/sup>                   Raise&nbsp;each factor to the power of&nbsp;2<\/p>\n\n\n\n<p>=<strong>36<\/strong>(p<sup>6<\/sup>)<sup>2  <\/sup>                         Simplify<\/p>\n\n\n\n<p>=36p<sup>(<strong>6 . 2<\/strong>)<\/sup>                     Simplify&nbsp;(p<sup>6<\/sup>)<sup>2<\/sup>,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n\n\n\n<p>=36p<sup><strong>12<\/strong>  <\/sup>                    Multiply<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85168\/477\/280\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png\" alt=\"\" class=\"wp-image-6848\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/51761\/183\/747\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-52.png\" alt=\"\" class=\"wp-image-6849\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-52.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-52-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-52-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Powers of monomials key notes: Definition: General Form: Rules for Multiplying Monomials: Rules for Dividing Monomials: Power of a Monomial Raised to a Power: Zero Exponent: Negative Exponent: Examples: Practice Tips: Learn with an example \u27a1\ufe0f Simplify.&nbsp; Express your answer using a single&nbsp;exponent. (10r4)4 The&nbsp;expression&nbsp;10r4&nbsp;is raised to the power of&nbsp;4.&nbsp;First, raise each factor to the<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/h-7-powers-of-monomials\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.7 Powers of monomials&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-154","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":12,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/154\/revisions"}],"predecessor-version":[{"id":17419,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/154\/revisions\/17419"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}