{"id":8779,"date":"2015-11-11T22:51:24","date_gmt":"2015-11-11T22:51:24","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8779"},"modified":"2015-11-30T01:09:25","modified_gmt":"2015-11-30T01:09:25","slug":"math-review-of-exponents","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2015\/11\/11\/math-review-of-exponents\/","title":{"rendered":"Math Review of Exponents"},"content":{"rendered":"<h3>Overview<\/h3>\n<p>Just as positive exponents direct how many times that a base number can be multiplied by itself, zero and negative exponents direct a similar relationship between the base number and its exponent.<\/p>\n<h3>Review of Positive Exponents<\/h3>\n<p>A nonzero expression that contains an exponent of any value has 2 parts, the base and the exponent. For example, an expression such as 2<sup>3<\/sup> has a base of 2 and an exponent of 3, so that 2 is a factor 3 times as in 2\u00b72\u00b72, or 8. If the expression contains a variable, such as x<sup>5<\/sup>, the base is a factor the number of times the exponent directs, such as x\u00b7x\u00b7x\u00b7x\u00b7x. If the nonzero number or the variable has an exponent of 1, it is the base number, such as 3<sup>1<\/sup> =3, 256<sup>1<\/sup> = 256, or y<sup>1<\/sup> = y.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/base-and-exponent.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-6954 aligncenter\" src=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/base-and-exponent.jpg\" alt=\"\" width=\"300\" height=\"255\" \/><\/a><\/p>\n<h3>Zero Exponents<\/h3>\n<p>Zero exponents follow a convention such that any nonzero base raised to the power of zero has a value of 1, such that 9<sup>0<\/sup> equals 1, z<sup>0<\/sup> equals 1, as long as z is not equal to zero, and 9245780<sup>0<\/sup> equals 1. Suppose the values of an exponent are expressed such that 2<sup>4<\/sup> = 16, because 2\u00b72\u00b72\u00b72 is 16. Dividing 2<sup>4<\/sup> by 2 equals 2<sup>3<\/sup> or 8, dividing 2<sup>3<\/sup> by 2 equals 2<sup>2<\/sup> or 4, dividing 2<sup>2<\/sup> by 2 equals 2<sup>1<\/sup> or 2, and dividing 2<sup>1<\/sup> by 2 equals 2<sup>0<\/sup>, or 1.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/zero-exponent.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-6954 aligncenter\" src=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/zero-exponent.jpg\" alt=\"\" width=\"300\" height=\"100\" \/><\/a><\/p>\n<h3>Negative Integer Exponents<\/h3>\n<p>Negative exponents are the reciprocal of positive exponents, such that if the base x is not equal to 0 and the exponent n is an integer, x<sup>-n<\/sup> equals 1\/x<sup>n<\/sup>. If 2<sup>-1 <\/sup>equals 1\/2, then continuing the pattern dividing by 2, dividing 2<sup>0<\/sup> by 2 equals 2<sup>-1<\/sup> or \u00bd. The number 1 divided by 2 equals \u00bd. Dividing 2<sup>-1<\/sup> by 2 equals 2<sup>-2<\/sup>, or \u00bc, because 2<sup>2<\/sup> equals 4. Dividing 2<sup>-2<\/sup> by 2 equals 2<sup>-3<\/sup> or 1\/8.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/negative-exponent.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-6954 aligncenter\" src=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2015\/11\/negative-exponent.jpg\" alt=\"\" width=\"270\" height=\"255\" \/><\/a><\/p>\n<h3>Simplifying Expressions<\/h3>\n<p>Expressions with exponents are simplified when there are no negative or zero exponents in the final expression. A negative exponent in the numerator of a fraction can always be moved to the denominator, and a zero exponent can always be simplified to equal 1.\u00a0 For example, an expression 3y<sup>-2<\/sup> can be simplified as 3\/y<sup>2<\/sup>.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/math-tutoring\/\">math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">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 Sheridan, WY: visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-sheridan-wyoming\/\">Tutoring in Sheridan, WY<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview Just as positive exponents direct how many times that a base number can be multiplied by itself, zero and negative exponents direct a similar relationship between the base number and its exponent. Review of Positive Exponents A nonzero expression that contains an exponent of any value has 2 parts, the base and the exponent. [&hellip;]<\/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":[1185,3862,3863],"class_list":["post-8779","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-negative-exponents","tag-positive-exponent","tag-zero-exponent"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8779","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=8779"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8779\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}