{"id":167615,"date":"2024-11-15T20:37:19","date_gmt":"2024-11-15T20:37:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167615"},"modified":"2024-11-15T20:37:21","modified_gmt":"2024-11-15T20:37:21","slug":"what-is-the-least-common-denominator-of-the-exponents","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/what-is-the-least-common-denominator-of-the-exponents\/","title":{"rendered":"What is the least common denominator of the exponents"},"content":{"rendered":"\n

What is the least common denominator of the exponents?<\/p>\n\n\n\n

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

To find the least common denominator (LCD) of exponents, we need to first clarify the question. The LCD of exponents typically refers to finding the least common multiple (LCM) of the denominators of fractional exponents in mathematical expressions. It is common in algebra when dealing with terms with fractional or rational exponents, and it helps simplify expressions or perform operations such as addition or subtraction.<\/p>\n\n\n\n

Step-by-Step Explanation:<\/h3>\n\n\n\n
    \n
  1. Understand the concept of exponents:<\/strong>
    Exponents indicate how many times a base number is multiplied by itself. When dealing with fractional exponents, the exponent represents both the root and the power. For example, ( x^{\\frac{m}{n}} ) means the (n)-th root of ( x ) raised to the power ( m ).<\/li>\n\n\n\n
  2. Example with fractional exponents:<\/strong>
    Consider the exponents ( \\frac{2}{3}, \\frac{4}{5}, \\frac{1}{6} ). These are fractional exponents, and we need to find the least common denominator (LCD) of their denominators, which are 3, 5, and 6.<\/li>\n\n\n\n
  3. Finding the least common multiple (LCM):<\/strong>
    The least common denominator of fractional exponents is the least common multiple of their denominators. To find the LCM of 3, 5, and 6:<\/li>\n<\/ol>\n\n\n\n
      \n
    • List the multiples of each number:\n
        \n
      • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, \u2026<\/li>\n\n\n\n
      • Multiples of 5: 5, 10, 15, 20, 25, 30, \u2026<\/li>\n\n\n\n
      • Multiples of 6: 6, 12, 18, 24, 30, \u2026<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • The smallest common multiple is 30<\/strong>.<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Conclusion:<\/strong>
          The least common denominator (LCD) of the exponents ( \\frac{2}{3}, \\frac{4}{5}, \\frac{1}{6} ) is 30. This means that when working with these fractional exponents, you can express them with a common denominator of 30, allowing for easier manipulation in operations like addition or subtraction.<\/li>\n<\/ol>\n\n\n\n

          In algebra, finding the LCD of exponents is an important step in simplifying expressions and performing calculations that involve fractional powers.<\/p>\n","protected":false},"excerpt":{"rendered":"

          What is the least common denominator of the exponents? The Correct Answer and Explanation is : To find the least common denominator (LCD) of exponents, we need to first clarify the question. The LCD of exponents typically refers to finding the least common multiple (LCM) of the denominators of fractional exponents in mathematical expressions. It […]<\/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-167615","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167615","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=167615"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167615\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}