<\/p>\n
Overview<\/strong><\/p>\n Rational exponents are an extension of the rules of exponents. They can be solved by applying those rules and often take more than one step.<\/p>\n What Is an Exponent?<\/strong><\/p>\n An exponent such as 32<\/sup> is a direction to multiply 3 by itself twice, such as 3\u22193, or 9.\u00a0 Similarly, an exponent such as 23<\/sup> is a direction to multiply 2 by itself 3 times, as 2\u22192\u22192.\u00a0 It is not the same as 2\u22193, which is 6.\u00a0 Therefore, a number such as an<\/sup> means to multiply a by itself n times.\u00a0 The rules of exponents have been extended so that x0<\/sup> equals 1, so that 50<\/sup> equals 1, 70<\/sup> equals 1, and so forth.\u00a0 By definition, x1<\/sup>is x by itself, so that 21<\/sup> equals 2, 51<\/sup> equals 5, and 100,521,3621<\/sup> equals 100,521,362.<\/p>\n What about Roots of Numbers?<\/strong><\/p>\n By definition, the root of a number is the inverse operation of multiplying by an exponent.\u00a0 If 32<\/sup> equals 9, the square root of 9 (\u221a9) is 3.\u00a0 Similarly, if 53<\/sup> means 5\u22195\u22195, then the cube root of 125 is 5.\u00a0 Also, if 24<\/sup> equals 16, then the fourth root of 16 is 2.\u00a0 In addition, (\u221a2)(\u221a2) is the same thing as saying (\u221a2)2<\/sup> or 2.\u00a0 That is also the same thing as 21<\/sup>.<\/p>\n What about Rational Exponents?<\/strong><\/p>\n By the rules of adding exponents, 22\u2219<\/sup>\u221924<\/sup> is the same thing as 26<\/sup>, or 22+4<\/sup>.\u00a0 Therefore, 2\u00bd<\/sup> \u2219 2\u00bd<\/sup>would be the same as 2\u00bd + \u00bd<\/sup> or 21<\/sup>.\u00a0 Now 21<\/sup> equals 2, and so does (\u221a2)2<\/sup>.\u00a0 By definition, the square root of any positive number n, when n>0, equals n1\/2<\/sup>.\u00a0 That definition can also be extended to roots other than square roots, such that n1\/3<\/sup> means the cube root of n.\u00a0 Therefore, 17281\/3<\/sup>is equal to the cube root of 1728, which is 12, because 123<\/sup> is 1728.<\/p>\n What about Other Fractional Exponents?<\/strong><\/p>\n The rules of defining fractional exponents such as 251\/2 <\/sup>mean that 251\/2<\/sup> is the same thing as the square root of 25, or 5.\u00a0 A fractional exponent as 253\/2<\/sup>, however, means (25 1\/2<\/sup>) 3<\/sup> or (\u221a25)3<\/sup>.\u00a0 It is a good rule to take the square root first, so the square root of 25 is 5, and 53<\/sup>is 125.\u00a0 Suppose the number were \u2013(16)1\/2<\/sup>.\u00a0 The square root of 16 is 4, and taking the negative would be -4.\u00a0 The square root of -16 is not a real number.<\/p>\n Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n SchoolTutoring Academy<\/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 Boca Raton, FL: visit Tutoring in Boca Raton, FL<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Overview Rational exponents are an extension of the rules of exponents. They can be solved by applying those rules and often take more than one step. What Is an Exponent? An exponent such as 32 is a direction to multiply 3 by itself twice, such as 3\u22193, or 9.\u00a0 Similarly, an exponent such as […]<\/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":[2],"tags":[2653,1498,2654],"class_list":["post-6864","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-rational-exponents","tag-real-numbers","tag-roots-of-numbers"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6864","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=6864"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6864\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6864"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6864"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}