Alg_Complete

Different indexes will give different evaluations so

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Unformatted text preview: Since we know how to evaluate rational exponents we also know how to evaluate radicals as the following set of examples shows. Example 2 Evaluate each of the following. (a) 16 and 4 16 [Solution] (b) 5 243 [Solution] (c) 4 1296 [Solution] (d) 3 -125 [Solution] (e) 4 -16 [Solution] Solution To evaluate these we will first convert them to exponent form and then evaluate that since we already know how to do that. (a) These are together to make a point about the importance of the index in this notation. Let’s take a look at both of these. 1 2 16 = 16 = 4 because 42 = 16 1 4 16 = 16 4 = 2 because 24 = 16 So, the index is important. Different indexes will give different evaluations so make sure that you don’t drop the index unless it is a 2 (and hence we’re using square roots). 1 5 243 = 243 = 3 because 35 = 243 (b) 5 (c) 4 (d) 3 -125 = ( -125 ) 3 = -5 (e) 4 -16 = ( -16 ) 4 1 1296 = 1296 4 = 6 because 64 = 1296 1 because ( -5 ) = -125 3 1 As we saw in the integer exponent section this does not have a real answ...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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