{"id":224945,"date":"2025-06-03T16:55:08","date_gmt":"2025-06-03T16:55:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224945"},"modified":"2025-06-03T16:55:10","modified_gmt":"2025-06-03T16:55:10","slug":"write-the-expression-12-2-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/write-the-expression-12-2-in-simplest-form\/","title":{"rendered":"Write the expression 12^-2 in simplest form."},"content":{"rendered":"\n

Write the expression 12^-2 in simplest form.<\/p>\n\n\n\n

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

Correct Answer:<\/strong> 12\u22122=1122=114412^{-2} = \\frac{1}{12^2} = \\frac{1}{144}<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/p>\n\n\n\n

The expression 12\u2212212^{-2} involves a negative exponent<\/strong>, which can seem confusing at first. To simplify it properly, we need to understand what a negative exponent means in mathematics.<\/p>\n\n\n\n

What Does a Negative Exponent Mean?<\/h3>\n\n\n\n

A negative exponent indicates reciprocal<\/strong>. Specifically, for any non-zero number aa and positive integer nn, a\u2212n=1ana^{-n} = \\frac{1}{a^n}<\/p>\n\n\n\n

This rule tells us that instead of multiplying the base repeatedly (as we do with positive exponents), we divide 1 by the base raised to the positive version of the exponent.<\/p>\n\n\n\n

Applying the Rule to 12\u207b\u00b2:<\/h3>\n\n\n\n

We use the rule: 12\u22122=112212^{-2} = \\frac{1}{12^2}<\/p>\n\n\n\n

Now, calculate 12212^2 (which means 12 \u00d7 12): 122=14412^2 = 144<\/p>\n\n\n\n

So, 12\u22122=114412^{-2} = \\frac{1}{144}<\/p>\n\n\n\n

This is the simplest form<\/strong> of the expression.<\/p>\n\n\n\n

Why Does This Rule Make Sense?<\/h3>\n\n\n\n

The rules for exponents are based on patterns that remain consistent across positive, zero, and negative exponents. For example: 122=144121=12120=112\u22121=11212\u22122=114412^2 = 144 \\\\ 12^1 = 12 \\\\ 12^0 = 1 \\\\ 12^{-1} = \\frac{1}{12} \\\\ 12^{-2} = \\frac{1}{144}<\/p>\n\n\n\n

Each time the exponent decreases by 1, we divide the previous result by 12. So moving from 120=112^0 = 1 to 12\u2212112^{-1}, we divide 1 by 12, getting 112\\frac{1}{12}. Then divide again by 12 to get 1144\\frac{1}{144}, which is 12\u2212212^{-2}.<\/p>\n\n\n\n

Understanding these patterns helps us simplify expressions with negative exponents easily and accurately.<\/p>\n\n\n\n

\n\n\n\n

Final Answer:<\/strong> 1144\\boxed{\\frac{1}{144}}<\/p>\n\n\n\n

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

Write the expression 12^-2 in simplest form. The Correct Answer and Explanation is: Correct Answer: 12\u22122=1122=114412^{-2} = \\frac{1}{12^2} = \\frac{1}{144} Explanation The expression 12\u2212212^{-2} involves a negative exponent, which can seem confusing at first. To simplify it properly, we need to understand what a negative exponent means in mathematics. What Does a Negative Exponent Mean? […]<\/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-224945","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224945","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=224945"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224945\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}