{"id":6628,"date":"2014-02-13T17:05:30","date_gmt":"2014-02-13T17:05:30","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6628"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"multiplication-and-division-of-monomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/02\/13\/multiplication-and-division-of-monomials\/","title":{"rendered":"Multiplication and Division of Monomials"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Monomials can be multiplied and divided like any other algebraic expression.\u00a0They can be simplified by applying the rules of exponents, if the bases are the same. It is not necessary to solve the equation for the values of the variables before operations can be performed.<\/p>\n

Multiplying Monomials with More than One Variable:<\/strong><\/p>\n

Applying the definition of multiplication, a problem such as 3a(2c) can be simplified by multiplying 3a times 2c.\u00a0 It is not necessary to solve for the values of a or c.\u00a0Because of the Commutative Property of Multiplication, the factors can be rearranged, so that the problem becomes 3\u22192\u2219a\u2219c, or 6ac.\u00a0The result is still a monomial.<\/p>\n

Multiplying Exponents:<\/strong><\/p>\n

If monomials are to be multiplied and the exponents have the same base, the exponents can be added to form the new monomial.\u00a0Suppose the problem were 4a3<\/sup>(9a2<\/sup>).\u00a0As before, use the Commutative Property of Multiplication to rearrange the factors, so that the problem becomes 4\u22199\u2219a\u2219a\u2219a\u2219a\u2219a, or 36a5<\/sup>.\u00a0If the problem were 2a2<\/sup>\u2219 13b4<\/sup>, the exponents couldn’t be combined.\u00a0The simplest form of the monomial would be 26a2<\/sup>b4<\/sup>.<\/p>\n

Powers of Monomials:<\/strong><\/p>\n

If a monomial is raised to a power, it can be simplified with a single exponent.\u00a0For example, (2x3<\/sup>)2<\/sup> actually means 2x3<\/sup>\u22192x3<\/sup>, or 4x6<\/sup>.\u00a0Similarly, (3y2<\/sup>z)4<\/sup> can be simplified as (34<\/sup>)(y2<\/sup>)4<\/sup>(z4<\/sup>) or 81y8<\/sup>z4<\/sup>. The general rule in algebraic terms is that (xa<\/sup>)b<\/sup> means xab<\/sup>.\u00a0Also, (xy)a<\/sup> means the same thing as xa<\/sup>ya<\/sup>, even when the monomial itself has a number of factors.<\/p>\n

Dividing Monomials:<\/strong><\/p>\n

The definition of division is multiplying by the inverse of the denominator, so that (6x)\/2 means the same as 6x \u22191\/2 or 3x.\u00a0If there are exponents in the numerator and the denominator, the exponents must be the same in order to simplify the expression.\u00a0An expression such as 4x3<\/sup>\/2x2<\/sup> can be simplified further as (4x3<\/sup>)(1\/2x-2<\/sup>) or (4\u22191\/2)(x3<\/sup>x-2<\/sup>).\u00a0One half of 4 is 2, and by the definition of multiplying exponents with the same base, x3<\/sup>x-2<\/sup> is the same thing as x3-2<\/sup> or x1<\/sup>, or 2x. Another way to state the rule in algebraic terms is that if x is real and not equal to 0, then xa<\/sup>\/xb<\/sup> means the same thing as xa-b<\/sup>.<\/p>\n

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Overview: Monomials can be multiplied and divided like any other algebraic expression.\u00a0They can be simplified by applying the rules of exponents, if the bases are the same. It is not necessary to solve the equation for the values of the variables before operations can be performed. Multiplying Monomials with More than One Variable: Applying the […]<\/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":[529,634,1146,1159],"class_list":["post-6628","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-division","tag-exponents","tag-monomials","tag-multiplication"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6628","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=6628"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6628\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}