{"id":7173,"date":"2014-06-27T16:17:41","date_gmt":"2014-06-27T16:17:41","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=7173"},"modified":"2014-12-02T08:25:28","modified_gmt":"2014-12-02T08:25:28","slug":"math-review-of-integers-as-exponents","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/06\/27\/math-review-of-integers-as-exponents\/","title":{"rendered":"Math Review of Integers as Exponents"},"content":{"rendered":"

Overview<\/h3>\n

Exponents are expressed as numbers or variables in superscript above a base number. When the exponent is equal to or greater than 2, it directs how many times the base number is to be multiplied. The numbers 1 and 0 are special exponents, and negative integers as exponents stand for reciprocal values.<\/p>\n

Definition<\/h3>\n

Exponential notation has two parts, a base b and an exponent n. It is usually written as bn<\/sup>, with the superscript to the right of the base, and sometimes as b^n, which essentially means to raise n to the exponent position. The meaning of exponential notation depends on the value of the exponent, whether it is 2 or greater, whether it is 1 or 0, or whether it is negative.<\/p>\n

Figure 1: An example of a base and exponent. 23<\/sup> = 2\u22192\u22192 = 8.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Exponents of Two or Greater<\/h3>\n

If the value of the exponent n is 2 or greater than 2, it is a direction to multiply the base b n times. Suppose the number is 37<\/sup>. That means 3\u22193\u22193\u22193\u22193\u22193\u22193, which equals 2187. If the number is n2<\/sup>, that means n\u2219n, or \u201cn squared\u201d. The area of a square is also n\u2219n. If the number is n3<\/sup>, that means n\u2219n\u2219n, or \u201cn cubed\u201d. The volume of a cube is also n\u2219n\u2219n.<\/p>\n

Exponents of One or Zero<\/h3>\n

Exponents of 1 or 0 follow a pattern. Any number n1<\/sup>, when n is greater than 0, is just the number itself, or n. Think of it as not multiplied at all. Therefore 31<\/sup> equals 3, 451<\/sup> equals 45, and 370,906,2321<\/sup> equals 370,906,232. Any number n with an exponent of 0, by convention, equals 1. The number 70<\/sup> equals 1, the number 2700<\/sup> equals 1, and the number 468,213,9960<\/sup> equals 1.<\/p>\n

Figure 2: The definition of zero exponents in symbol form.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Negative Exponents<\/h3>\n

Negative integers as exponents also follow a pattern. Any exponent b-n<\/sup>, when b is not 0 means the same thing as 1\/bn<\/sup>. For example, 3-2<\/sup> means the same thing as 1\/32<\/sup>, or 1\/9. If the base is 10, the exponents in decimal notation follow a familiar pattern, so that 100<\/sup> equals 1, 101<\/sup> equals 10, 102 <\/sup>equals 100, 103<\/sup> equals 1000, and so on. Also, 10-1<\/sup>, equals 1\/10, or 0.1, 10-2<\/sup> equals 1\/100, or 0.01, 10-3<\/sup> equals 1\/1000 or 0.001, and so on.<\/p>\n

Figure 3: The definition of negative exponents in symbol form.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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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 Moncton, NB, Canada: visit Tutoring in Moncton, NB, Canada<\/a><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Exponents are expressed as numbers or variables in superscript above a base number. When the exponent is equal to or greater than 2, it directs how many times the base number is to be multiplied. The numbers 1 and 0 are special exponents, and negative integers as exponents stand for reciprocal values. Definition Exponential […]<\/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":[634,1185],"class_list":["post-7173","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponents","tag-negative-exponents"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7173","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=7173"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7173\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}