{"id":8810,"date":"2016-01-01T23:01:39","date_gmt":"2016-01-01T23:01:39","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8810"},"modified":"2016-01-01T23:01:39","modified_gmt":"2016-01-01T23:01:39","slug":"math-review-of-division-of-exponents","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-division-of-exponents\/","title":{"rendered":"Math Review of Division of Exponents"},"content":{"rendered":"

Overview<\/h3>\n

As division is the inverse of multiplication, so division of exponents is the inverse of multiplication of exponents.\u00a0 There are properties for the division of exponents similar to the properties for the multiplication of exponents.<\/p>\n

Quotient of Powers<\/h3>\n

Recall that finding a product of powers with the same base is expressed by the rule in algebra language of xm<\/sup>xn<\/sup> = xm +n<\/sup>.\u00a0 This concept was developed by using the definition of exponents as repeated multiplication.\u00a0 If x3<\/sup> is x\u00b7x\u00b7x and x2 <\/sup>is x\u00b7x, then x3<\/sup>x2<\/sup> is (x\u00b7x\u00b7x)(x\u00b7x).\u00a0 What about (x3<\/sup>)\/(x2<\/sup>)?\u00a0 That also can be simplified by using the definition of exponents, as (x\u00b7x\u00b7x)\/(x\u00b7x) is x3-2<\/sup> or x.\u00a0 In the language of algebra, xm<\/sup>\/xn<\/sup> equals xm-n<\/sup>, when x is a real number not equal to zero and m and n are integers.<\/p>\n

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Positive Power of a Quotient<\/h3>\n

Recall also that any expression (ab)n<\/sup> can be expanded to an<\/sup>bn<\/sup>.\u00a0 For example, an expression such as (3x)3<\/sup> means 3\u00b73\u00b73\u00b7x\u00b7x\u00b7x or 27x3<\/sup>. \u00a0Similarly, a quotient such as (2\/5)4<\/sup> means (2\/5)(2\/5)(2\/5)(2\/5) or (24<\/sup>)\/(54<\/sup>).\u00a0 The quotient is in simplest form with the exponents, or it can be multiplied out as 16\/625.\u00a0 In the language of algebra, (a\/b)n<\/sup> equals an<\/sup>\/bn<\/sup>, if a and b are real numbers not equal to zero, and n is a positive integer.<\/p>\n

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Negative Power of a Quotient<\/h3>\n

Remember that x-n<\/sup> is the reciprocal of xn<\/sup> or 1\/xn<\/sup>.\u00a0 For example, 5-3<\/sup> is the same thing as 1\/53<\/sup> or 1\/125.\u00a0 Similarly, the reciprocal of 5\/6 is 1\/(5\/6) or 6\/5.\u00a0 Suppose that the value of x is the fraction a\/b.\u00a0 In that case, x-n<\/sup> would equal 1\/(a\/b)n<\/sup>, or 1\/(an<\/sup>\/bn<\/sup>), or bn<\/sup>\/an<\/sup>, which is the reciprocal of an<\/sup>\/bn<\/sup>.\u00a0 In the language of algebra, if a and b are real numbers not equal to zero and n is a positive integer, then (a\/b)-n<\/sup> is equal to (b\/a)n<\/sup>, which is equal to bn<\/sup>\/an<\/sup>.<\/p>\n

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Applications of Exponents<\/h3>\n

Exponents are often used in scientific notation to express numbers that are very large or very small.\u00a0 For example, the distance from the Sun to the Earth is about 9.3 x 107<\/sup> miles. However, the size of an average dust particle is about 7.53 x 10-10<\/sup> kg.\u00a0 Exponents are also used in other applications, including economics, measurement, engineering, and accounting.<\/p>\n

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Overview As division is the inverse of multiplication, so division of exponents is the inverse of multiplication of exponents.\u00a0 There are properties for the division of exponents similar to the properties for the multiplication of exponents. Quotient of Powers Recall that finding a product of powers with the same base is expressed by the rule […]<\/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":[3878,1185,2732],"class_list":["post-8810","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-division-of-exponents","tag-negative-exponents","tag-reciprocals"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8810","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=8810"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8810\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8810"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8810"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}