{"id":5775,"date":"2013-04-26T07:45:17","date_gmt":"2013-04-26T07:45:17","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5775"},"modified":"2014-12-02T08:27:03","modified_gmt":"2014-12-02T08:27:03","slug":"exponents-and-scientific-notation","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/04\/26\/exponents-and-scientific-notation\/","title":{"rendered":"Exponents and Scientific Notation"},"content":{"rendered":"

\u00a0Overview:\u00a0 Exponents and Variables<\/strong><\/p>\n

An exponent is a signal for how many times to multiply a number over again.\u00a0 For example, 26<\/sup> means the same thing as 2 \u2219 2 \u2219 2 \u2219 2 \u2219 2 \u2219 2 = 64.\u00a0 If a variable has an exponent, for example, a2<\/sup>, the exponent 2 just means a \u2219 a. When evaluating variables, it is important to understand the meaning of exponents and how they relate in the number sentence.<\/p>\n

Bases and Exponents<\/strong><\/p>\n

A number such as 26<\/sup> or x12<\/sup> has two parts, the base, and the exponent.\u00a0 The 2 is the base, and it is raised to the sixth power.\u00a0 Similarly, the x is the base, and it is raised to the 12th power.\u00a0 The bases must be the same in order to combine exponents, and to reduce the monomial to its simplest form.\u00a0 Therefore, a monomial such as 2c3<\/sup>x2<\/sup> is already factored as much as it can be and is in its simplest form.<\/p>\n

Multiplying and Dividing Exponents<\/strong><\/p>\n

If a monomial is 2c3<\/sup>c2<\/sup>, it is not factored into its simplest form, but is in two parts with the same base that can be combined, 2c3<\/sup> and c2<\/sup>.\u00a0 They can be multiplied to form a new monomial, 2c3<\/sup> \u2219 c \u2219 c , or 2c5<\/sup>, by a property of exponents that states that for any real integer x, when a and b are positive integers, xa<\/sup>\u2219 xb<\/sup> = xa +b<\/sup>.\u00a0 That is one can multiply exponents with the same base by adding exponents.\u00a0 \u00a0Dividing exponents works similarly, by subtracting exponents when they are the same bases.\u00a0 Therefore , for any real number x, when x is not equal to 0, and a and b are positive integers, xa<\/sup>\/xb<\/sup> = xa-b<\/sup>.\u00a0 The exponent in the\u00a0 denominator is always subtracted from the exponent in the numerator.<\/p>\n

Negative Exponents<\/strong><\/p>\n

Negative exponents follow the logic of dividing exponents of like bases.\u00a0 By applying the property for dividing exponents (The Quotient Property), x 8<\/sup>\/x10<\/sup>, would equal x8-10<\/sup>, or x-2<\/sup>. What is x-2<\/sup>?\u00a0 Take a step back to solve the division problem another way.\u00a0 Using this method, x8<\/sup>\/x10<\/sup> can be expressed as x8<\/sup>\/x8<\/sup>\u22191\/x2<\/sup>.\u00a0 Therefore, x-2<\/sup> means the same thing as 1\/x2<\/sup>.\u00a0 Generalizing to another definition, for any real number x, when x is not equal to 0, and a is a positive integer, x-a<\/sup> means the same thing as i\/xa<\/sup>.<\/p>\n

Scientific Notation<\/strong><\/p>\n

Scientific notation is an application of the rules about exponents, and are a way to express very large numbers (such as the distances to planets, stars, and galaxies) and very small numbers (such as the size of microbes, viruses, and atoms.\u00a0 When the number is large, the power of 10 will have a positive exponent, but when it is small, the power of 10 will have a negative exponent.\u00a0 For example, if the nearest star outside the solar system is about 4 X 1013<\/sup> km from the earth, it is 40,000,000,000,000 km from the earth.\u00a0 Similarly, a helium atom has a diameter of 2.2 x 10-8<\/sup> cm, or 0.00000022 cm.<\/p>\n

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\u00a0Overview:\u00a0 Exponents and Variables An exponent is a signal for how many times to multiply a number over again.\u00a0 For example, 26 means the same thing as 2 \u2219 2 \u2219 2 \u2219 2 \u2219 2 \u2219 2 = 64.\u00a0 If a variable has an exponent, for example, a2, the exponent 2 just means a […]<\/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":[178,634,1185,1593],"class_list":["post-5775","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-base","tag-exponents","tag-negative-exponents","tag-scientific-notation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5775","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=5775"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5775\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}