{"id":249818,"date":"2025-07-10T05:27:45","date_gmt":"2025-07-10T05:27:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249818"},"modified":"2025-07-10T05:27:47","modified_gmt":"2025-07-10T05:27:47","slug":"select-all-the-expressions-that-equal-6-10","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/select-all-the-expressions-that-equal-6-10\/","title":{"rendered":"Select all the expressions that equal 6^-10"},"content":{"rendered":"\n

Select all the expressions that equal 6^-10<\/p>\n\n\n\n

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

The expression 6\u2212106^{-10}6\u221210 represents the reciprocal of 6106^{10}610, or 1610\\frac{1}{6^{10}}6101\u200b. To find equivalent expressions, we need to manipulate this expression in ways that maintain its value.<\/p>\n\n\n\n

Here are possible equivalent expressions for 6\u2212106^{-10}6\u221210:<\/p>\n\n\n\n

    \n
  1. 1610\\frac{1}{6^{10}}6101\u200b<\/strong>
    This is the direct mathematical definition of negative exponents. 6\u2212106^{-10}6\u221210 means 111 divided by 6106^{10}610, so 1610\\frac{1}{6^{10}}6101\u200b is equivalent.<\/li>\n\n\n\n
  2. (1\/6)10(1\/6)^{10}(1\/6)10<\/strong>
    This expression uses the rule that (ab)\u2212c=(a\u2212c)b(a^b)^{-c} = (a^{-c})^b(ab)\u2212c=(a\u2212c)b. In this case, the base of 666 is raised to the negative exponent, and you can rewrite it as (1\/6)10(1\/6)^{10}(1\/6)10, which is clearly equivalent to 1610\\frac{1}{6^{10}}6101\u200b.<\/li>\n\n\n\n
  3. 6\u22125\u00d76\u221256^{-5} \\times 6^{-5}6\u22125\u00d76\u22125<\/strong>
    Using the law of exponents, am\u00d7an=am+na^m \\times a^n = a^{m+n}am\u00d7an=am+n. Here, we can break down 6\u2212106^{-10}6\u221210 as 6\u22125\u00d76\u221256^{-5} \\times 6^{-5}6\u22125\u00d76\u22125, since \u22125+(\u22125)=\u221210-5 + (-5) = -10\u22125+(\u22125)=\u221210.<\/li>\n\n\n\n
  4. 165\u00d7165\\frac{1}{6^5} \\times \\frac{1}{6^5}651\u200b\u00d7651\u200b<\/strong>
    Similar to the previous example, 6\u2212106^{-10}6\u221210 can be written as the product of two terms 165\u00d7165\\frac{1}{6^5} \\times \\frac{1}{6^5}651\u200b\u00d7651\u200b, since 6\u22125\u00d76\u22125=6\u2212106^{-5} \\times 6^{-5} = 6^{-10}6\u22125\u00d76\u22125=6\u221210. This is just another way of writing 1610\\frac{1}{6^{10}}6101\u200b.<\/li>\n<\/ol>\n\n\n\n

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

    The concept of negative exponents tells us that a\u2212n=1ana^{-n} = \\frac{1}{a^n}a\u2212n=an1\u200b. So, when you see a negative exponent, you’re really working with the reciprocal of that base raised to the positive exponent. Any manipulation of this form (like splitting the exponent into smaller parts or converting it into a fraction) will lead to equivalent expressions.<\/p>\n\n\n\n

    Thus, all the above examples are valid ways to express 6\u2212106^{-10}6\u221210 because they either break down or rearrange the base and exponent while keeping the value the same.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Select all the expressions that equal 6^-10 The Correct Answer and Explanation is: The expression 6\u2212106^{-10}6\u221210 represents the reciprocal of 6106^{10}610, or 1610\\frac{1}{6^{10}}6101\u200b. To find equivalent expressions, we need to manipulate this expression in ways that maintain its value. Here are possible equivalent expressions for 6\u2212106^{-10}6\u221210: Explanation: The concept of negative exponents tells us that […]<\/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-249818","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249818","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=249818"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249818\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}