{"id":165763,"date":"2024-11-12T20:08:54","date_gmt":"2024-11-12T20:08:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165763"},"modified":"2024-11-12T20:08:56","modified_gmt":"2024-11-12T20:08:56","slug":"what-is-x-squared-divided-by-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/12\/what-is-x-squared-divided-by-x\/","title":{"rendered":"What is x squared divided by x"},"content":{"rendered":"\n

What is x squared divided by x?<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The expression ( x^2 \\div x ) simplifies to ( x ).<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To understand why ( x^2 \\div x = x ), let\u2019s break down the mathematical rules at play:<\/p>\n\n\n\n

    \n
  1. Understanding Exponents<\/strong>:<\/li>\n<\/ol>\n\n\n\n
      \n
    • An exponent tells us how many times to multiply a number by itself. For example, ( x^2 ) means ( x \\times x ).<\/li>\n\n\n\n
    • In general, ( x^n ) (where ( n ) is a positive integer) represents ( x ) multiplied by itself ( n ) times.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Dividing Terms with Exponents<\/strong>:<\/li>\n<\/ol>\n\n\n\n
          \n
        • When we divide terms that have the same base (like ( x )), we subtract their exponents. This is called the quotient rule for exponents<\/em>, which states:
          [
          \\frac{x^a}{x^b} = x^{a – b}
          ]<\/li>\n\n\n\n
        • Here, ( a = 2 ) and ( b = 1 ), so ( x^2 \\div x^1 = x^{2 – 1} = x^1 ) or simply ( x ).<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Applying the Rule to ( x^2 \\div x )<\/strong>:<\/li>\n<\/ol>\n\n\n\n
              \n
            • Substitute into the rule: ( x^2 \\div x = x^{2 – 1} = x ).<\/li>\n<\/ul>\n\n\n\n
                \n
              1. Another Way to Look at It<\/strong>:<\/li>\n<\/ol>\n\n\n\n
                  \n
                • You can also break down ( x^2 \\div x ) as:
                  [
                  \\frac{x \\times x}{x}
                  ]<\/li>\n\n\n\n
                • Here, one ( x ) on the top cancels with the ( x ) on the bottom, leaving you with just ( x ).<\/li>\n<\/ul>\n\n\n\n
                    \n
                  1. Key Insight<\/strong>:<\/li>\n<\/ol>\n\n\n\n
                      \n
                    • Dividing two terms with the same base simplifies the expression because of exponent subtraction. It is a shortcut for expressing repeated multiplication and allows us to simplify complex expressions efficiently.<\/li>\n<\/ul>\n\n\n\n

                      In summary, ( x^2 \\div x = x ) due to the rule for dividing exponents with the same base, where we subtract the exponents. This rule is fundamental in algebra and helps simplify expressions across various mathematical contexts.<\/p>\n","protected":false},"excerpt":{"rendered":"

                      What is x squared divided by x? The Correct Answer and Explanation is : The expression ( x^2 \\div x ) simplifies to ( x ). Explanation: To understand why ( x^2 \\div x = x ), let\u2019s break down the mathematical rules at play: In summary, ( x^2 \\div x = x ) due […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-165763","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165763","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=165763"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165763\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}