Stitz-Zeager_College_Algebra_e-book

X x 4 2 to graph y 25 5 we start with the basic

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Unformatted text preview: st property which makes compositions of roots and powers delicate. This is especially true when we use exponential notation for radicals. Recall the following definition. Definition 5.5. Let x be a real number, m an integera and n a natural number. 1 m • xn a √ n √ x and is defined whenever n x is defined. √ √m √m = ( n x) = n xm , whenever ( n x) is defined. • xn = Recall this means m = 0, ±1, ±2, . . . The rational exponents defined in Definition 5.5 behave very similarly to the usual integer exponents 3/2 from Elementary Algebra with one critical exception. Consider the expression x2/3 . Applying 3/2 23 the usual laws of exponents, we’d be tempted to simplify this as x2/3 = x 3 · 2 = x1 = x. √ 2 However, if we substitute x = −1 and apply Definition 5.5, we find (−1)2/3 = 3 −1 = (−1)2 = 1 √3 3/2 3/2 = x. If we take so that (−1)2/3 = 13/2 = 1 = 13 = 1. We see in this case that x2/3 the time to rewrite x2/3 x2/3 3/2 3/2 = with radicals, we see √ 3 x 2 3/2 = √...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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