To see why this is consider the following 1 8 x 10

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Unformatted text preview: to this rule and that is square root. For square roots we have, 2 a= a In other words, for square roots we typically drop the index. Let’s do a couple of examples to familiarize us with this new notation. Example 1 Write each of the following radicals in exponent form. (a) 4 16 (b) 10 8 x (c) Solution (a) 16 = 16 4 (b) 10 x2 + y2 1 4 1 8 x = ( 8 x )10 1 (c) x2 + y 2 = ( x2 + y 2 ) 2 As seen in the last two parts of this example we need to be careful with parenthesis. When we convert to exponent form and the radicand consists of more than one term then we need to enclose the whole radicand in parenthesis as we did with these two parts. To see why this is consider the following, 1 8 x 10 From our discussion of exponents in the previous sections we know that only the term immediately to the left of the exponent actually gets the exponent. Therefore, the radical form of this is, 1 10 8 x = 8 10 x ¹ 10 8 x So, we once again see that parenthesis are very important in this class. Be careful with them. © 2007 Paul Dawkins 16 College Algebra...
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