{"id":8805,"date":"2015-12-27T23:23:05","date_gmt":"2015-12-27T23:23:05","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8805"},"modified":"2015-12-28T19:13:37","modified_gmt":"2015-12-28T19:13:37","slug":"math-review-of-multiplication-of-exponents","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-multiplication-of-exponents\/","title":{"rendered":"Math Review of Multiplication of Exponents"},"content":{"rendered":"

Overview<\/h3>\n

Exponents are used as a type of shorthand directing how many times that a base number is multiplied by itself. Exponential expressions are useful when working with very large or very small numbers, as in scientific notation. \u00a0\u00a0Like other numbers and variables, exponential expressions can be multiplied following certain rules.<\/p>\n

Review of Simplifying Expressions<\/h3>\n

If there are negative exponents in an expression, it is not simplified. The expression x-3<\/sup> can be defined as 1\/x3<\/sup>.\u00a0 Similarly, if the same base is used more than once in an expression, it is not simplified.\u00a0 Suppose the expression is x2<\/sup>x.\u00a0 That actually means x\u00b7x\u00b7x, or x3<\/sup>.\u00a0 Also, powers that are raised to powers are not simplified, such as [x5<\/sup>]2<\/sup>.\u00a0 If any coefficients have common factors, those common factors must be simplified.\u00a0 For example, (15a2<\/sup>)\/ (10b3<\/sup>) can be simplified to (3a2<\/sup>)\/ (2b3<\/sup>) because 15 and 10 have a common factor of 5.<\/p>\n

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Products of Powers<\/h3>\n

Since an exponent stands for how many times a base is multiplied by itself, the rule for multiplying exponents can be discovered by showing each power as repeated multiplication.\u00a0 If the expression is y3<\/sup>y2<\/sup>, that can be expanded as y\u00b7y\u00b7y\u00b7y\u00b7y, or y5<\/sup>.\u00a0 The product of the powers can be found by adding the exponents, as 3 +2 = 5.\u00a0 However, the bases must be the same in order for the exponents to be added. In the language of algebra, for any real number a not equal to zero, am<\/sup>\u00b7an<\/sup> = am+n<\/sup>.<\/p>\n

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Powers of Powers<\/h3>\n

Expressions such as [x5<\/sup>]2<\/sup> actually mean x5<\/sup>\u00b7x5<\/sup>, or (x\u00b7x\u00b7x\u00b7x\u00b7x) (x\u00b7x\u00b7x\u00b7x\u00b7x), by using the meaning of exponents as repeated multiplication.\u00a0 The product of powers of powers can be found by multiplying the exponents, as 5\u00b72 equals 10.\u00a0 In the language of algebra, for any real number a not equal to zero, (am<\/sup>)n<\/sup>=amn<\/sup>.\u00a0 The way to know whether to add or multiply the exponents is to expand the expression to repeated multiplication.\u00a0 For example, z3<\/sup>z4<\/sup> means z\u00b7z\u00b7z\u00b7z\u00b7z\u00b7z\u00b7z, or z7<\/sup>, while (z3<\/sup>)4<\/sup> means (z3<\/sup>)(z3<\/sup>)(z3<\/sup>)(z3<\/sup>), or (z\u00b7z\u00b7z)(z\u00b7z\u00b7z)(z\u00b7z\u00b7z)(z\u00b7z\u00b7z) or z12<\/sup>.<\/p>\n

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Powers of Products<\/h3>\n

An expression such as q5<\/sup> only involves one component, the variable q.\u00a0 However, an expression such as (3z)3<\/sup> has two components, the coefficient 3 and the variable z.\u00a0 It can be expanded as (3z)(3z)(3z), or 3\u00b73\u00b73\u00b7z\u00b7z\u00b7z, or 33<\/sup>z3<\/sup>, or 27z3<\/sup>.\u00a0 In the language of algebra, (ab)n<\/sup>, for any real number a and b not equal to zero and n as an integer, (ab)n<\/sup> equals an<\/sup>bn<\/sup>.<\/p>\n

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Overview Exponents are used as a type of shorthand directing how many times that a base number is multiplied by itself. Exponential expressions are useful when working with very large or very small numbers, as in scientific notation. \u00a0\u00a0Like other numbers and variables, exponential expressions can be multiplied following certain rules. Review of Simplifying Expressions […]<\/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":[634,3877,3282],"class_list":["post-8805","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponents","tag-multiplication-of-exponents","tag-simplifying-exponents"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8805","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=8805"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8805\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}