{"id":178,"date":"2022-04-12T09:47:42","date_gmt":"2022-04-12T09:47:42","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=178"},"modified":"2025-02-10T04:34:57","modified_gmt":"2025-02-10T04:34:57","slug":"i-1-understanding-exponents","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/i-1-understanding-exponents\/","title":{"rendered":"I.1 Understanding exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Understanding exponents<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-0c45b07820a2b22c9dece8248a82d021\" style=\"color:#000060\"><strong>Definition of Exponents<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Explain that exponents represent repeated multiplication. For instance, ana^nan means aaa multiplied by itself nnn times.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4c93c1d30f1de3bc8243ac3b7ca61e0f\" style=\"color:#000060\"><strong>Basic Exponent Rules<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Multiplication Rule: a<sup>m<\/sup> \u00d7 a<sup>n<\/sup> = a<sup>m+n<\/sup><\/li>\n\n\n\n<li>Division Rule: a<sup>m<\/sup>\/a<sup>n<\/sup> = a<sup>m\u2212n<\/sup><\/li>\n\n\n\n<li>Power of a Power: (a<sup>m<\/sup>)<sup>n<\/sup> = a<sup>m\u22c5n<\/sup><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f99e3f9345881d1b16c68ff37622a6f8\" style=\"color:#000060\"><strong>Negative Exponents<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Introduce the concept that a<sup>\u2212n<\/sup> is 1\/a<sup>n<\/sup>\u200b. Explain why negative exponents result in fractions.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e9b0a6f51a03272b76f1ee52d015d916\" style=\"color:#000060\"><strong>Zero Exponent<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Discuss why a<sup>0<\/sup> = 1, emphasizing the rule and its applications.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-cf85a311f68a33e4ef74e46844259c98\" style=\"color:#000060\"><strong>Exponentiation of Zero and One<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Cover 0<sup>n<\/sup> = 0 (except 0<sup>0<\/sup>) and 1<sup>n<\/sup> = 1.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5aac62c82627e44a9b5370535153928c\" style=\"color:#000060\"><strong>Exponential Notation<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Teach how to convert between exponential notation and standard notation (e.g., 10<sup>3<\/sup> = 1000).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-a1dd05ac7f3003ffe8c2ee0a20655cdb\" style=\"color:#000060\"><strong>Application in Real-Life Scenarios<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Provide examples where exponents are used in real-world contexts, such as compound interest, scientific notation, and geometric sequences.<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#c7ebf6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>An&nbsp;exponent tells you how many times to use the base as a&nbsp;factor.<\/p>\n\n\n\n<p>For&nbsp;example:<\/p>\n\n\n\n<p>8<sup>2<\/sup> = 8 . 8<\/p>\n\n\n\n<p>8<sup>3<\/sup> = 8 . 8 . 8 <\/p>\n\n\n\n<p>8<sup>4<\/sup> = 8 . 8 . 8 . 8<\/p>\n\n\n\n<p>8<sup>5<\/sup> = 8 . 8 . 8 . 8 . 8<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#daffd8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>An&nbsp;exponent tells you how many times to use the base as a&nbsp;factor.<\/p>\n\n\n\n<p>For&nbsp;example:<\/p>\n\n\n\n<p>4<sup>2<\/sup> = 4 . 4<\/p>\n\n\n\n<p>4<sup>3<\/sup> = 4 . 4 . 4 <\/p>\n\n\n\n<p>4<sup>4<\/sup> = 4 . 4 . 4 . 4<\/p>\n\n\n\n<p>4<sup>5<\/sup> = 4 . 4 . 4 . 4 . 4<\/p>\n<\/div><\/div>\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\" style=\"background-color:#dad3fb\"><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\">\ud83c\udfaf <strong>Write&nbsp;the expression using an&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>3 . 3<\/p>\n<\/div><\/div>\n\n\n\n<p>3&nbsp;is used as a factor&nbsp;2&nbsp;times, so the base is&nbsp;3&nbsp;and the exponent is&nbsp;2.<\/p>\n\n\n\n<p>3 . 3 = 3<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f4eed4\"><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\">\ud83c\udfaf <strong>Write&nbsp;the expression using an&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>2 . 2<\/p>\n<\/div><\/div>\n\n\n\n<p>2&nbsp;is used as a factor&nbsp;2&nbsp;times, so the base is&nbsp;2&nbsp;and the exponent is&nbsp;2.<\/p>\n\n\n\n<p>2 . 2 = 2<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#facaca\"><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\">\ud83c\udfaf <strong>Write&nbsp;the expression using an&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p>7 . 7<\/p>\n<\/div><\/div>\n\n\n\n<p>7&nbsp;is used as a factor&nbsp;2&nbsp;times, so the base is&nbsp;7&nbsp;and the exponent is&nbsp;2.<\/p>\n\n\n\n<p>7 . 7 = 7<sup>2<\/sup><\/p>\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<\/div><\/div>\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\/84634\/029\/190\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-274.png\" alt=\"\" class=\"wp-image-7435\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-274.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-274-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-274-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-274-400x400.png 400w\" 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\/86155\/166\/864\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-282.png\" alt=\"\" class=\"wp-image-7436\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-282.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-282-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-282-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-282-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Understanding exponents Key notes: Definition of Exponents: Explain that exponents represent repeated multiplication. For instance, ana^nan means aaa multiplied by itself nnn times. Basic Exponent Rules: Negative Exponents: Introduce the concept that a\u2212n is 1\/an\u200b. Explain why negative exponents result in fractions. Zero Exponent: Discuss why a0 = 1, emphasizing the rule and its applications.<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/i-1-understanding-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;I.1 Understanding exponents&#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,"footnotes":""},"class_list":["post-178","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=178"}],"version-history":[{"count":14,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions"}],"predecessor-version":[{"id":15625,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions\/15625"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}