{"id":353,"date":"2022-04-13T09:08:00","date_gmt":"2022-04-13T09:08:00","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=353"},"modified":"2024-10-17T10:37:58","modified_gmt":"2024-10-17T10:37:58","slug":"u-7-power-rule","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/u-7-power-rule\/","title":{"rendered":"U.7 Power rule"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Power rule<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8d847c2fc40915b48ea748b80671e362\" style=\"color:#74008b\"><strong>Key notes : <\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>Power Rule Overview<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Definition<\/strong>: The Power Rule is a basic rule of differentiation in calculus that helps find the derivative of a function in the form of f(x)=x<sup>n<\/sup> where n is any real number.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Formula<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"544\" height=\"102\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-5.png\" alt=\"\" class=\"wp-image-15597\" style=\"width:593px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-5.png 544w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-5-300x56.png 300w\" sizes=\"auto, (max-width: 544px) 100vw, 544px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>Key Points<\/strong><\/h3>\n\n\n\n<ol class=\"has-large-font-size wp-block-list\">\n<li><strong>Basic Concept<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The Power Rule states that to differentiate a power of x, multiply the power by the coefficient (which is 1 if none is given) and then reduce the power by 1.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Example<\/strong>: <\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"111\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-6.png\" alt=\"\" class=\"wp-image-15598\" style=\"width:549px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-6.png 634w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-6-300x53.png 300w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/figure><\/div>\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:#a7cee9\"><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 class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>(u<sup>8<\/sup>)<sup>4<\/sup> = ______<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;u<sup>8<\/sup>&nbsp;is raised to the power of&nbsp;4.&nbsp;Multiply the&nbsp;exponents.(u<sup>8<\/sup>)<sup>4<\/sup>=u(<strong><sup>8 . 4<\/sup><\/strong>)    Simplify&nbsp;(u<sup>8<\/sup>)<sup>4<\/sup>,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n\n\n\n<p>=u<strong><sup>32<\/sup><\/strong>        Multiply<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9eee94\"><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 class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>(m<sup>7<\/sup>)<sup>2<\/sup> = __________<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;m<sup>7<\/sup>&nbsp;is raised to the power of&nbsp;4.&nbsp;Multiply the&nbsp;exponents.<\/p>\n\n\n\n<p>(m<sup>7<\/sup>)<sup>2<\/sup>=m(<strong><sup>7 . <\/sup><\/strong><sup>2<\/sup>)    Simplify&nbsp;(m<sup>7<\/sup>)<sup>2<\/sup>,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n\n\n\n<p>=m<sup>14 <\/sup>       Multiply<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e9a0a0\"><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 class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>(r<sup>8<\/sup>)<sup>5<\/sup>=__________<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;r<sup>8<\/sup>&nbsp;is raised to the power of&nbsp;5.&nbsp;Multiply the&nbsp;exponents.  <\/p>\n\n\n\n<p>   (r<sup>8<\/sup>)<sup>5<\/sup>=r(<strong><sup>8.5<\/sup><\/strong>) Simplify&nbsp;(r8)5,&nbsp;remembering to multiply the&nbsp;exponents<\/p>\n\n\n\n<p>=r<strong><sup>40<\/sup><\/strong>        Multiply<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/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\/79945\/100\/164\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133.png\" alt=\"\" class=\"wp-image-8100\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-133-150x150.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\/79801\/274\/104\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png\" alt=\"\" class=\"wp-image-8101\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Power rule Key notes : Power Rule Overview Formula Key Points Learn with an example Simplify.&nbsp;Express your answer using a single&nbsp;exponent. (u8)4 = ______ The&nbsp;expression&nbsp;u8&nbsp;is raised to the power of&nbsp;4.&nbsp;Multiply the&nbsp;exponents.(u8)4=u(8 . 4) Simplify&nbsp;(u8)4,&nbsp;remembering to multiply the&nbsp;exponents =u32 Multiply Simplify.&nbsp;Express your answer using a single&nbsp;exponent. (m7)2 = __________ The&nbsp;expression&nbsp;m7&nbsp;is raised to the power of&nbsp;4.&nbsp;Multiply the&nbsp;exponents.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/u-7-power-rule\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.7 Power rule&#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-353","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/353","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=353"}],"version-history":[{"count":16,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/353\/revisions"}],"predecessor-version":[{"id":15599,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/353\/revisions\/15599"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}