{"id":96,"date":"2022-04-12T12:06:08","date_gmt":"2022-04-12T12:06:08","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=96"},"modified":"2025-10-29T06:29:18","modified_gmt":"2025-10-29T06:29:18","slug":"f-4-exponents-with-negative-bases","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-4-exponents-with-negative-bases\/","title":{"rendered":"F.4 Exponents with negative bases"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Exponents with negative bases<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3JiD7rBU\/5dVRRKF_XbPsiRbQZZ8GmA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3JiD7rBU&#x2F;5dVRRKF_XbPsiRbQZZ8GmA&#x2F;watch?utm_content=DAG3JiD7rBU&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-09eb8d27d0d70f35bd20b1cf47293f11\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\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> What is a Negative Base?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>negative base<\/strong> means the base number is less than zero.<\/li>\n\n\n\n<li>Example: (\u22122),(\u22125),(\u221210)etc.<\/li>\n\n\n\n<li>The rules of exponents still apply, but we must be careful with brackets.<\/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> Rules to Remember<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Even Exponents make the result positive<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\u2212a)<sup>even<\/sup>=(+)<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u22123)<sup>2<\/sup> = (\u22123) \u00d7 (\u22123) = 9<\/li>\n<\/ul>\n\n\n\n<p><strong>Odd Exponents keep the result negative<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\u2212a)<sup>odd<\/sup>=(\u2212)<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u22123)3=(\u22123)\u00d7(\u22123)\u00d7(\u22123)=\u221227<\/li>\n<\/ul>\n\n\n\n<p><strong>Brackets matter!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\u22123)<sup>2=<\/sup>9( (because both factors are included inside brackets).<\/li>\n\n\n\n<li>\u22123<sup>2<\/sup>=\u22129 (because only 3<sup>2<\/sup>=9, then negative sign is applied outside).<\/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>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(\u22124)<sup>2<\/sup>=16<\/li>\n\n\n\n<li>(\u22124)<sup>3<\/sup>=\u221264<\/li>\n\n\n\n<li>(\u22122)<sup>5=<\/sup>\u221232<\/li>\n\n\n\n<li>(\u22122)<sup>6<\/sup>=64<\/li>\n\n\n\n<li>\u22122<sup>4<\/sup>=\u221216<\/li>\n<\/ol>\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><strong>Key Points<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>With brackets<\/strong> \u2192 exponent applies to the whole negative number.<\/li>\n\n\n\n<li><strong>Without brackets<\/strong> \u2192 exponent applies only to the positive number; the negative sign stays outside.<\/li>\n\n\n\n<li><strong>Even powers<\/strong> \u2192 always positive.<\/li>\n\n\n\n<li><strong>Odd powers <\/strong>\u2192 always negative.<\/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><strong>Practice Problems<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(\u22125)<sup>2=<\/sup>?<\/li>\n\n\n\n<li>(\u22127)<sup>3<\/sup>=?<\/li>\n\n\n\n<li>\u22126<sup>2<\/sup> =?<\/li>\n\n\n\n<li>(\u22122<sup>)4<\/sup>=?<\/li>\n\n\n\n<li>(\u22123)<sup>5<\/sup>=?<\/li>\n<\/ol>\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>\ud83d\udc49 <strong>Summary<\/strong>:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">When working with <strong>negative bases in exponents<\/strong>, always check <strong>if brackets are present<\/strong> and <strong>whether the power is even or odd<\/strong>.<\/p>\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\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-44cc1ce5ea2cb900d727b9fc3dc4f236\" style=\"background-color:#ed87fa\"><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-text-color has-background has-link-color wp-elements-1dee199dda5685147835efa39f82a4ee\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-83eb93ee26f26851367fc5456453f3a3\" style=\"color:#b00012\"><strong>Evaluate<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\">(-4)<sup>3<\/sup>&nbsp;=&nbsp;___<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is \u20134 and the exponent is 3. Use \u20134 as a factor 3 times.<\/p>\n\n\n\n<p>(-4)<sup>3<\/sup> = (\u20134) \u00b7 (\u20134) \u00b7 (\u20134)<\/p>\n\n\n\n<p>          = \u201364<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-6a2862cbf8dbd434dc62052859c01f2e\" style=\"background-color:#86dcf9\"><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-text-color has-background has-link-color wp-elements-7bf85ea6bacd6d8562a12197809008de\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-83eb93ee26f26851367fc5456453f3a3\" style=\"color:#b00012\"><strong>Evaluate<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\">-1<sup>3<\/sup>&nbsp;=&nbsp;___<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is 1 (not \u20131) and the exponent is 3. Use 1 as a factor 3 times. The negative sign stays out in front.<\/p>\n\n\n\n<p>-1<sup>3<\/sup> = \u2013(1 \u00b7 1 \u00b7 1)<\/p>\n\n\n\n<p>      = \u20131<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-563d4e577e9963fde8917cca56cab97c\" style=\"background-color:#bffa87\"><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-text-color has-background has-link-color wp-elements-1793b0a4d8b84b434b0c5c7f336d5d60\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-9f5957e02b090bb6396d44a0517b16a6\" style=\"color:#b00012\"><strong>Evaluate.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><sup>(-3)<sup>3<\/sup>&nbsp;=<\/sup>___<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is \u20133 and the exponent is 3. Use \u20133 as a factor 3 times.<\/p>\n\n\n\n<p>(-3)<sup>3<\/sup>&nbsp;= (\u20133) \u00b7 (\u20133) \u00b7 (\u20133)<\/p>\n\n\n\n<p>         = \u201327<\/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<\/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\/77973\/280\/455\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-294.png\" alt=\"\" class=\"wp-image-9574\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-294.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-294-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-294-150x150.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\/78206\/317\/548\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-301.png\" alt=\"\" class=\"wp-image-9575\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-301.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-301-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-301-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exponents with negative bases Design by Delta publications Key Notes : What is a Negative Base? Rules to Remember Even Exponents make the result positive Odd Exponents keep the result negative Brackets matter! Examples Key Points Practice Problems \ud83d\udc49 Summary: When working with negative bases in exponents, always check if brackets are present and whether<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-4-exponents-with-negative-bases\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.4 Exponents with negative bases&#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-96","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\/96","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=96"}],"version-history":[{"count":28,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/96\/revisions"}],"predecessor-version":[{"id":22044,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/96\/revisions\/22044"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}