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CHAPTER_ppt_10_2 - 10.2 Rational Exponents Exponents with...

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§ 10.2 Rational Exponents
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Exponents with Rational Numbers So far, we have only worked with integer exponents. In this section, we extend exponents to rational numbers as a shorthand notation when using radicals. The same rules for working with exponents will still apply.
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Recall that a cube root is defined so that a b b a = = 3 3 if only However, if we let b = a 1/3 , then ( 29 a a a a b = = = = 1 3 3 / 1 3 3 / 1 3 ) ( Since both values of b give us the same a , 3 3 / 1 a a = Understanding a 1/ n n n a a = / 1 n a If n is a positive integer greater than 1 and is a real number, then 1 Definition of n a
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Use radical notation to write the following. Simplify if possible. 3 3 81 4 4 4 = = = 4 / 1 81 ( 29 = 5 / 1 10 32 x 2 5 10 5 5 10 2 2 32 x x x = = ( 29 = 3 / 1 7 16 x 3 2 3 3 6 3 3 7 4 3 7 2 2 2 2 2 16 x x x x x x = = = Using Radical Notation Example:
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 5
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