{"id":90,"date":"2022-04-12T12:05:14","date_gmt":"2022-04-12T12:05:14","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=90"},"modified":"2025-10-07T05:39:31","modified_gmt":"2025-10-07T05:39:31","slug":"f-1-understanding-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-1-understanding-exponents\/","title":{"rendered":"F.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<figure class=\"wp-block-video\"><video autoplay controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Understanding-exponents.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-7464115d112791a83a98a59c10102309\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong> What are Exponents?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">An exponent refers to the number of times a number (called the base) is multiplied by itself.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It is written in the form: <strong>a^n<\/strong>, where:<\/li>\n\n\n\n<li><strong>a<\/strong> is the base.<\/li>\n\n\n\n<li><strong>n<\/strong> is the exponent (or power).<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Basic Terminology<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Base<\/strong>: The number being multiplied.<\/li>\n\n\n\n<li><strong>Exponent<\/strong>: The number showing how many times the base is used as a factor.<\/li>\n\n\n\n<li class=\"has-normal-font-size\"><strong>Example<\/strong>: In <strong>3^4<\/strong>, 3 is the base, and 4 is the exponent. This means 3 \u00d7 3 \u00d7 3 \u00d7 3 = 81.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong> <strong>Understanding Powers of 10<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exponents are commonly used with the base 10 to represent large or small numbers.<\/li>\n\n\n\n<li>Example: <strong>10^3 = 10 \u00d7 10 \u00d7 10 = 1000<\/strong>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Exponent Rules<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Product Rule<\/strong>: When multiplying two numbers with the same base, add the exponents.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <strong>a^m \u00d7 a^n = a^(m+n)<\/strong>.<\/li>\n\n\n\n<li>Example: <strong>2^3 \u00d7 2^2 = 2^(3+2) = 2^5 = 32<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Quotient Rule<\/strong>: When dividing two numbers with the same base, subtract the exponents.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <strong>a^m \u00f7 a^n = a^(m\u2212n)<\/strong>.<\/li>\n\n\n\n<li>Example: <strong>5^6 \u00f7 5^2 = 5^(6-2) = 5^4 = 625<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Power Rule<\/strong>: When raising an exponent to another exponent, multiply the exponents.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <strong>(a^m)^n = a^(m\u00d7n)<\/strong>.<\/li>\n\n\n\n<li>Example: <strong>(2^3)^2 = 2^(3\u00d72) = 2^6 = 64<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Zero Exponent Rule<\/strong>: Any non-zero number raised to the power of 0 is equal to 1.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <strong>a^0 = 1<\/strong> (if a \u2260 0).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Negative Exponent Rule<\/strong>: A number with a negative exponent represents the reciprocal of the number raised to the positive exponent.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <strong>a^(-n) = 1\/a^n<\/strong>.<\/li>\n\n\n\n<li>Example: <strong>2^(-3) = 1\/2^3 = 1\/8<\/strong>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong> <strong>Working with Large and Small Numbers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Exponents make it easier to express large or small numbers in scientific notation.<\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-normal-font-size wp-elements-daa7b8014617c20d5da0d406254d8911\"><strong>Example: 3 \u00d7 10^6<\/strong> represents <strong>3,000,000<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-cdfdae77473d09a24f745c0a67b1796d\" style=\"background-color:#3b3b03\"><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 has-link-color wp-elements-01ec62e4b7934b0c774febb8d2933650\" style=\"color:#d90000\">Write the expression using exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center\">42 \u00b7 42 \u00b7 42 \u00b7 59<\/p>\n<\/div><\/div>\n\n\n\n<p>Start with the given expression.<\/p>\n\n\n\n<p>42 \u00b7 42 \u00b7 42 \u00b7 59<\/p>\n\n\n\n<p>Write the 42&#8217;s using exponents. 42 is used as a factor 3 times, so its exponent is 3.<\/p>\n\n\n\n<p><strong>42<sup><strong>3<\/strong><\/sup><\/strong><\/p>\n\n\n\n<p>Write the 59&#8217;s using exponents. 59 is used as a factor 1 time, so its exponent is 1. When a number has an exponent of one, you don&#8217;t need to write the exponent.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">42<sup>3<\/sup>&nbsp;\u00b7&nbsp;<strong>59<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-2484a6966a07782eb04a65cae41a77cd\" style=\"background-color:#00615e\"><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 has-link-color wp-elements-01ec62e4b7934b0c774febb8d2933650\" style=\"color:#d90000\">Write the expression using exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">7 \u00b7 7 \u00b7 7<\/p>\n<\/div><\/div>\n\n\n\n<p>Start with the given expression.<\/p>\n\n\n\n<p>7 \u00b7 7 \u00b7 7<\/p>\n\n\n\n<p>Write the 7&#8217;s using exponents. 7 is used as a factor 3 times, so its exponent is 3.<\/p>\n\n\n\n<p class=\"has-huge-font-size\"><strong>7<sup><strong>3<\/strong><\/sup><\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-6a924e9a9423b9e2b50851c611e31138\" style=\"background-color:#780070\"><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 has-link-color wp-elements-01ec62e4b7934b0c774febb8d2933650\" style=\"color:#d90000\">Write the expression using exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\">33 \u00b7 33 \u00b7 58 \u00b7 58 \u00b7 58<\/p>\n<\/div><\/div>\n\n\n\n<p>Start with the given expression.<\/p>\n\n\n\n<p>33 \u00b7 33 \u00b7 58 \u00b7 58 \u00b7 58<\/p>\n\n\n\n<p>Write the 33&#8217;s using exponents. 33 is used as a factor 2 times, so its exponent is 2.<\/p>\n\n\n\n<p><strong>33<sup><strong>2<\/strong><\/sup><\/strong><\/p>\n\n\n\n<p>Write the 58&#8217;s using exponents. 58 is used as a factor 3 times, so its exponent is 3.<\/p>\n\n\n\n<p>33<sup>2<\/sup>&nbsp;\u00b7&nbsp;<strong>58<sup><strong>3<\/strong><\/sup><\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/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\/77088\/859\/464\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-297.png\" alt=\"\" class=\"wp-image-9583\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-297.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-297-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-297-150x150.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\/77036\/242\/782\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-304.png\" alt=\"\" class=\"wp-image-9584\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-304.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-304-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-304-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Understanding exponents Key Notes: What are Exponents? An exponent refers to the number of times a number (called the base) is multiplied by itself. Basic Terminology Understanding Powers of 10 Exponent Rules Product Rule: When multiplying two numbers with the same base, add the exponents. Quotient Rule: When dividing two numbers with the same base,<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-1-understanding-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-90","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/90","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=90"}],"version-history":[{"count":31,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/90\/revisions"}],"predecessor-version":[{"id":21732,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/90\/revisions\/21732"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=90"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}