{"id":6603,"date":"2013-12-26T20:56:58","date_gmt":"2013-12-26T20:56:58","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6603"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"math-review-of-positive-and-negative-exponents","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/12\/26\/math-review-of-positive-and-negative-exponents\/","title":{"rendered":"Math Review of Positive and Negative Exponents"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Exponents, or powers, are shorthand for repeated multiplication of the same number, variable, or expression.\u00a0 They are especially useful to describe variables and expressions that are multiplied over and over again.<\/p>\n<p><strong>How Do Positive Exponents Work?<\/strong><\/p>\n<p>Positive exponents are a signal to multiply the base that number of times.\u00a0 For example, if the number is 10<sup>3<\/sup>, 10 should be multiplied as 10 \u2219 10 \u2219 10, or 1000.\u00a0 If the variable is x<sup>9<\/sup>, the variable x should be multiplied by itself 9 times, as x\u2219x\u2219x\u2219x\u2219x\u2219x\u2219x\u2219x\u2219x.\u00a0 If the expression is (3x)<sup>3<\/sup>, then 3x is multiplied by itself 3 times, as 3x\u22193x\u22193x, or 9x<sup>3<\/sup>.<\/p>\n<p><strong>What If the Exponent Is 1 or 0?<\/strong><\/p>\n<p>If the exponent is 1, that means that the base is multiplied 1 time.\u00a0 In other words, the base is just itself.\u00a0 If 10<sup>1<\/sup> is 10, then x<sup>1<\/sup> is x, and (8x)<sup>1<\/sup> is 8x.\u00a0 In algebraic terms, any number n<sup>1<\/sup> equals n.\u00a0 By definition, any number with an exponent of 0 is equal to 1.\u00a0 Therefore, 10<sup>0<\/sup> equals 1, (4y)<sup>0<\/sup> equals 1, and z<sup>0<\/sup> equals 1, as long as none of the variables are equal to 0.<\/p>\n<p><strong>What Are Negative Exponents?<\/strong><\/p>\n<p>Negative exponents are shorthand for the inverse of the number with a positive exponent.\u00a0 For example, 10<sup>-2<\/sup> is 1\/10<sup>2<\/sup>, or 1\/100. Similarly, z<sup>-4<\/sup> is 1\/z<sup>4<\/sup>.\u00a0 For the algebraic definition to work, the number must be a positive real number and it cannot be equal to zero.\u00a0 That is because dividing by zero is undefined.<\/p>\n<p><strong>What About Simplifying Expressions?<\/strong><\/p>\n<p>When an expression has a negative exponent, it can be simplified by either using the definition of a negative exponent or solving the exponent.\u00a0 For example, y<sup>-9<\/sup> equals 1\/y<sup>9<\/sup>, just as (-5)<sup>-3<\/sup> is the same thing as -1\/5<sup>3<\/sup>, which can be solved as -1\/125.\u00a0 In some equations, it is an advantage to simplify the expression.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/pre-algebra-tutoring\/\">Pre-Algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy&#8217;s<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Erie, PA visit:<a href=\"https:\/\/schooltutoring.com\/tutoring-in-erie-pennsylvania\/\"> Tutoring in Erie, PA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Exponents, or powers, are shorthand for repeated multiplication of the same number, variable, or expression.\u00a0 They are especially useful to describe variables and expressions that are multiplied over and over again. How Do Positive Exponents Work? Positive exponents are a signal to multiply the base that number of times.\u00a0 For example, if the number [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[13],"tags":[1185,1364],"class_list":["post-6603","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-negative-exponents","tag-positive-exponents"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6603"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6603\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}