{"id":188,"date":"2022-04-12T09:49:14","date_gmt":"2022-04-12T09:49:14","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=188"},"modified":"2025-02-10T09:23:45","modified_gmt":"2025-02-10T09:23:45","slug":"i-6-evaluate-numerical-expressions-involving-exponents","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/i-6-evaluate-numerical-expressions-involving-exponents\/","title":{"rendered":"I.6 Evaluate numerical expressions involving exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Evaluate numerical expressions involving exponents<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b;text-transform:capitalize\">Key notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9a8c691c21b26e52b7123092597bd8ab\" style=\"color:#000060\"><strong>Definition of Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>An exponent represents repeated multiplication of a base number.<\/li>\n\n\n\n<li>Example: 3<sup>4<\/sup> = 3 \u00d7 3 \u00d7 3 \u00d7 3 = 81.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c0e17e31447dc8cf0ddebe4c344c889e\" style=\"color:#000060\"><strong>Parts of an Exponential Expression<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Base<\/strong>: The number being multiplied (e.g., 3 in 3<sup>4<\/sup>).<\/li>\n\n\n\n<li><strong>Exponent<\/strong>: The small number above the base indicating the number of times to multiply (e.g., 4 in 3<sup>4<\/sup>).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e7e0a33e8e7f535918e2bcfa28899c72\" style=\"color:#000060\"><strong>Evaluating Expressions with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Follow the order of operations (PEMDAS\/BODMAS).<\/li>\n\n\n\n<li>Compute exponents before multiplication, division, addition, or subtraction.<\/li>\n\n\n\n<li>Example: 2 + 3<sup>2<\/sup> = 2 + 9 = 11.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-a5ae7ad96e00c1bf8568d82bf6bf0ad0\" style=\"color:#000060\"><strong>Properties of Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Product Rule<\/strong>: a<sup>m<\/sup> \u00d7 a<sup>n<\/sup> = a<sup>m+n<\/sup>.<\/li>\n\n\n\n<li><strong>Quotient Rule<\/strong>: a<sup>m<\/sup> \u00f7 a<sup>n<\/sup> = a<sup>m\u2212n<\/sup>, where m>n.<\/li>\n\n\n\n<li><strong>Power Rule<\/strong>: (a<sup>m<\/sup>)<sup>n<\/sup> = a<sup>m\u00d7n<\/sup>.<\/li>\n\n\n\n<li><strong>Zero Exponent Rule<\/strong>: a<sup>0<\/sup> = 1 (any nonzero number raised to 0 is 1).<\/li>\n\n\n\n<li><strong>Negative Exponent Rule<\/strong>: a<sup>\u2212n<\/sup> = 1a<sup>n<\/sup>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-ae7627a307a8afbe43830127e936727d\" style=\"color:#000060\"><strong>Evaluating Expressions with Different Operations<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Example: 4<sup>3<\/sup> \u2212 2<sup>2<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>4<sup>3<\/sup> = 4 \u00d7 4 \u00d7 4 = 64.<\/li>\n\n\n\n<li>2<sup>2<\/sup> = 2 \u00d7 2 = 4.<\/li>\n\n\n\n<li>64 \u2212 4 = 60.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-bbb06effecc08ad049d0119df1853c86\" style=\"color:#000060\"><strong>Using Exponents in Real-Life Problems<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Square and cube numbers in geometry and physics.<\/li>\n\n\n\n<li>Exponential growth in populations and finance.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-cb7bf5938c80e2102a4292daca7c1cc3\" style=\"color:#000060\"><strong>Common Mistakes to Avoid<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Misinterpreting aba^bab as a\u00d7ba \\times ba\u00d7b.<\/li>\n\n\n\n<li>Forgetting the order of operations.<\/li>\n\n\n\n<li>Incorrectly applying exponent rules.<\/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:#f5b3b3\"><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 class=\"has-text-color\" style=\"color:#b00012\">\u27a1\ufe0f <strong>Evaluate&nbsp;the&nbsp;expression. <\/strong><\/p>\n\n\n\n<p>2<sup>2<\/sup> \u00d7 1<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression .<\/p>\n\n\n\n<p>2<sup>2<\/sup> x 1<\/p>\n\n\n\n<p>This&nbsp;expression has an exponent. It also has multiplication. The order of operations says to evaluate the exponent before&nbsp;multiplying.<\/p>\n\n\n\n<p>2<sup>2<\/sup> \u00d7 1<\/p>\n\n\n\n<p>= <strong>4 <\/strong>\u00d7 1<\/p>\n\n\n\n<p>Now,&nbsp;multiply.<\/p>\n\n\n\n<p>4 \u00d7 1<\/p>\n\n\n\n<p>= <strong>4<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The value of the expression is 4.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e2d7fb\"><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\">\u27a1\ufe0f <strong>Evaluate&nbsp;the&nbsp;expression.<\/strong><\/p>\n\n\n\n<p>5 \u00d7 3<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>5 <strong>\u00d7 <\/strong>3<strong><sup>2<\/sup><\/strong><\/p>\n\n\n\n<p>This&nbsp;expression has an exponent. It also has multiplication. The order of operations says to evaluate the exponent before&nbsp;multiplying.<\/p>\n\n\n\n<p>5 \u00d7 3<sup>2<\/sup><\/p>\n\n\n\n<p>= 5 \u00d7 <strong>9<\/strong><\/p>\n\n\n\n<p>Now,&nbsp;multiply.<\/p>\n\n\n\n<p>5 \u00d7 9<\/p>\n\n\n\n<p>= <strong>45<\/strong><\/p>\n\n\n\n<p>The value of the expression is 45.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f2f9cb\"><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\">\u27a1\ufe0f <strong>Evaluate&nbsp;the&nbsp;expression.<\/strong><\/p>\n\n\n\n<p>3 \u2013 4<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;identify the operations in the&nbsp;expression.<\/p>\n\n\n\n<p>3 \u2013 4<strong><sup>2<\/sup><\/strong><\/p>\n\n\n\n<p>This&nbsp;expression has an exponent. It also has subtraction. The order of operations says to evaluate the exponent before&nbsp;subtracting.<\/p>\n\n\n\n<p>3 \u2013 4<sup>2<\/sup> <\/p>\n\n\n\n<p>= 3 \u2013 <strong>16<\/strong><\/p>\n\n\n\n<p>Now,&nbsp;subtract.<\/p>\n\n\n\n<p>3 \u2013 16 <\/p>\n\n\n\n<p>= \u201313<\/p>\n\n\n\n<p>The&nbsp;value of the expression is&nbsp;\u2013 13.<\/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\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\/85888\/129\/671\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-279.png\" alt=\"\" class=\"wp-image-7450\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-279.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-279-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-279-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-279-400x400.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\/86164\/444\/146\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-287.png\" alt=\"\" class=\"wp-image-7451\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-287.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-287-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-287-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-287-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate numerical expressions involving exponents Key notes: Definition of Exponents Parts of an Exponential Expression Evaluating Expressions with Exponents Properties of Exponents Evaluating Expressions with Different Operations Example: 43 \u2212 22 Using Exponents in Real-Life Problems Common Mistakes to Avoid Learn with an example \u27a1\ufe0f Evaluate&nbsp;the&nbsp;expression. 22 \u00d7 1 First,&nbsp;identify the operations in the&nbsp;expression .<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/i-6-evaluate-numerical-expressions-involving-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;I.6 Evaluate numerical expressions involving 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-188","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188","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=188"}],"version-history":[{"count":16,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188\/revisions"}],"predecessor-version":[{"id":15639,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188\/revisions\/15639"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}