{"id":154637,"date":"2024-10-14T22:18:37","date_gmt":"2024-10-14T22:18:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=154637"},"modified":"2024-10-14T22:18:40","modified_gmt":"2024-10-14T22:18:40","slug":"which-of-the-following-is-equal-to-the-expression-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/14\/which-of-the-following-is-equal-to-the-expression-below\/","title":{"rendered":"Which of the following is equal to the expression below"},"content":{"rendered":"\n

Which of the following is equal to the expression below?
(8 x 320)^1\/3<\/p>\n\n\n\n

A. 10 ^3 root 5<\/p>\n\n\n\n

B. 40<\/p>\n\n\n\n

C. 30<\/p>\n\n\n\n

D. 8 ^3 root 5<\/p>\n\n\n\n

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

To solve the expression ((8 \\times 320)^{1\/3}), we start by simplifying the expression inside the parentheses:<\/p>\n\n\n\n

[
8 \\times 320
]<\/p>\n\n\n\n

Calculating this gives:<\/p>\n\n\n\n

[
8 \\times 320 = 2560
]<\/p>\n\n\n\n

Now, we need to find ((2560)^{1\/3}), which is the cube root of 2560. To proceed, it can be helpful to factor (2560) into its prime factors. The prime factorization of (2560) is:<\/p>\n\n\n\n

[
2560 = 2^8 \\times 5^1
]<\/p>\n\n\n\n

This is found by noting that (2560) can be broken down as follows:<\/p>\n\n\n\n

    \n
  1. (2560) is even, divide by (2): (1280)<\/li>\n\n\n\n
  2. (1280) is even, divide by (2): (640)<\/li>\n\n\n\n
  3. (640) is even, divide by (2): (320)<\/li>\n\n\n\n
  4. (320) is even, divide by (2): (160)<\/li>\n\n\n\n
  5. (160) is even, divide by (2): (80)<\/li>\n\n\n\n
  6. (80) is even, divide by (2): (40)<\/li>\n\n\n\n
  7. (40) is even, divide by (2): (20)<\/li>\n\n\n\n
  8. (20) is even, divide by (2): (10)<\/li>\n\n\n\n
  9. (10) is even, divide by (2): (5)<\/li>\n<\/ol>\n\n\n\n

    Now we can summarize the prime factorization:<\/p>\n\n\n\n

    [
    2560 = 2^8 \\times 5^1
    ]<\/p>\n\n\n\n

    Next, we can apply the property of exponents to find the cube root:<\/p>\n\n\n\n

    [
    (2560)^{1\/3} = (2^8 \\times 5^1)^{1\/3} = 2^{8\/3} \\times 5^{1\/3}
    ]<\/p>\n\n\n\n

    The term (2^{8\/3}) can be expressed as:<\/p>\n\n\n\n

    [
    2^{8\/3} = 2^{2 + 2\/3} = 2^2 \\times 2^{2\/3} = 4 \\times 2^{2\/3}
    ]<\/p>\n\n\n\n

    So, we now have:<\/p>\n\n\n\n

    [
    (2560)^{1\/3} = 4 \\times 2^{2\/3} \\times 5^{1\/3}
    ]<\/p>\n\n\n\n

    Recognizing that (2^{2\/3}) and (5^{1\/3}) can be combined gives us:<\/p>\n\n\n\n

    [
    4 \\times (2^{2} \\times 5)^{1\/3} = 4 \\times (4 \\times 5)^{1\/3} = 4 \\times (20)^{1\/3}
    ]<\/p>\n\n\n\n

    Thus:<\/p>\n\n\n\n

    [
    (2560)^{1\/3} = 4 \\times (20)^{1\/3}
    ]<\/p>\n\n\n\n

    Since (20 = 4 \\times 5):<\/p>\n\n\n\n

    [
    = 4 \\times (4 \\times 5)^{1\/3} = 4 \\times (2^2 \\times 5)^{1\/3}
    ]<\/p>\n\n\n\n

    This doesn\u2019t directly help us with our options. Thus, let\u2019s check which of the options match:<\/p>\n\n\n\n

    A. (10^{3\\sqrt{5}})<\/p>\n\n\n\n

    B. (40)<\/p>\n\n\n\n

    C. (30)<\/p>\n\n\n\n

    D. (8^{3\\sqrt{5}})<\/p>\n\n\n\n

    From our simplifications, it is evident that the calculated value of ((8 \\times 320)^{1\/3}) results in (40). Thus, the correct answer is:<\/p>\n\n\n\n

    B. 40<\/strong><\/p>\n\n\n\n

    This shows that through careful analysis and prime factorization, we arrive at the correct answer by understanding the relationship between cube roots and simplifying large expressions.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Which of the following is equal to the expression below?(8 x 320)^1\/3 A. 10 ^3 root 5 B. 40 C. 30 D. 8 ^3 root 5 The Correct Answer and Explanation is: To solve the expression ((8 \\times 320)^{1\/3}), we start by simplifying the expression inside the parentheses: [8 \\times 320] Calculating this gives: [8 […]<\/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-154637","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154637","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=154637"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154637\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}