{"id":3337,"date":"2012-08-29T20:28:49","date_gmt":"2012-08-29T20:28:49","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=3337"},"modified":"2014-12-02T08:32:05","modified_gmt":"2014-12-02T08:32:05","slug":"number-theory-exponents-powers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/number-theory-exponents-powers\/","title":{"rendered":"Number Theory: Exponents (Powers)"},"content":{"rendered":"

The distance between the Sun and the earth is 149,600,000,000m. It\u2019s very difficult to read and even to write also. To make these type of numbers easy to read and write we use exponents. Using exponents the same number can be written as 1496×108<\/sup>m. \u00a0Here we read 108<\/sup> as 10 raised to the power 8. An exponent<\/em> <\/strong>is mathematically defined as follows.<\/p>\n

\u201cThe exponent of a number shows how many times that number is multiplied in a product\u201d.<\/strong><\/p>\n

An exponent is also called as power<\/em><\/strong>.<\/p>\n

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

22<\/sup> = 2×2<\/p>\n

35<\/sup> = 3x3x3x3x3<\/p>\n

Laws of indices: <\/span><\/strong>\u00a0For any real numbers x and y,<\/p>\n

(1)\u00a0\u00a0\u00a0 xm<\/sup> x xn<\/sup> = x m+n<\/sup><\/p>\n

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

22<\/sup> x 23<\/sup> = 4 x 8 = 32 = 25<\/sup><\/p>\n

This property can be remembered as \u201cThe powers of same bases must be added in case of multiplication\u201d.<\/p>\n

(2)\u00a0\u00a0\u00a0 xm<\/sup> \/ xn<\/sup> = x m-n<\/sup><\/p>\n

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

23<\/sup> \/ 22<\/sup> = 8 \/ 4 = 2 = 21<\/sup> = 23-2<\/sup><\/p>\n

This property can be remembered as \u201cThe powers of same bases must be subtracted in order in case of division\u201d.<\/p>\n

(3)\u00a0\u00a0\u00a0 x-m <\/sup>= 1\/xm<\/sup><\/p>\n

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

2-3<\/sup>= 1\/23<\/sup> = 1\/8<\/p>\n

This property can be remembered as \u201ca negative (positive) power can be converted into negative (positive) by taking its reciprocal.\u201d<\/p>\n

(4)\u00a0\u00a0\u00a0 x0<\/sup> =1, where x \u2260 0.<\/p>\n

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

30<\/sup> = 31-1 <\/sup>= 31<\/sup>\/31<\/sup> = 1<\/p>\n

This property can be remembered as \u201cAny number raised to zero is always one\u201d.<\/p>\n

(5)\u00a0\u00a0\u00a0 (xm<\/sup>)n<\/sup> = xmn<\/sup><\/p>\n

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

(32<\/sup>)3<\/sup> = 93<\/sup> = 243=36<\/sup>.<\/p>\n

This property can be remembered as \u201cThe powers of same base must be multiplied\u201d.<\/p>\n

(6)\u00a0\u00a0\u00a0 xm<\/sup> x ym<\/sup> = (xy)m<\/sup><\/p>\n

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

23<\/sup> x 33<\/sup> = 8 x 27 = 216 = 63<\/sup>= (2×3)3<\/sup><\/p>\n

This property can be remembered as \u201cThe product of different bases of same multiplied can be written as the product of bases raised to the same power\u201d.<\/p>\n

 <\/p>\n

Still need help with Mathematics? pPlease read more about our Mathematics tutoring services<\/a>.<\/p>\n

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 Parlier visit: Tutoring in Parlier.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

The distance between the Sun and the earth is 149,600,000,000m. It\u2019s very difficult to read and even to write also. To make these type of numbers easy to read and write we use exponents. Using exponents the same number can be written as 1496×108m. \u00a0Here we read 108 as 10 raised to the power 8. […]<\/p>\n","protected":false},"author":19,"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":[631,823,1010,1371,2197,2552],"class_list":["post-3337","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponent","tag-how-do-i-use-exponents","tag-laws","tag-power","tag-what-is-an-exponent","tag-when-are-exponents-useful"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3337","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3337"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3337\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}