46 CHAPTER R Review of Basic Concepts EXAMPLE 7 Using the Definition of a1/n Evaluate each expression. (a) 361/2 (b) -1001/2 (c) -122521/2 (d) 6251/4 (e) 1-129621/4 (f) -12961/4 (g) 1-2721/3 (h) -321/5 SOLUTION (a) 361/2 = 6 because 62 = 36. (b) -1001/2 = -10 (c) -122521/2 = -15 (d) 6251/4 = 5 (e) 1-129621/4 is not a real number. (f) -12961/4 = -6 (g) 1-2721/3 = -3 (h) -321/5 = -2 S Now Try Exercises 73, 75, and 79. The notation am/n must be defined in such a way that all the previous rules for exponents still hold. For power rule 1 to hold, 1a1/n2m must equal am/n. Therefore, am/n is defined as follows. The Expression a m/n Let m be any integer, n be any positive integer, and a be any real number for which a1/n is a real number. a m/n = 1a1/n2m S Now Try Exercises 83, 85, and 87. EXAMPLE 8 Using the Definition of am/n Evaluate each expression. (a) 1252/3 (b) 327/5 (c) -813/2 (d) 1-2722/3 (e) 16-3/4 (f) 1-425/2 SOLUTION (a) 1252/3 = 11251/322 = 52 = 25 (b) 327/5 = 1321/527 = 27 = 128 (c) -813/2 = -1811/223 = -93 = -729 (d) 1-2722/3 = 31-2721/342 = 1-322 = 9 (e) 16-3/4 = 1 163/4 = 1 1161/423 = 1 23 = 1 8 (f) 1-425/2 is not a real number. This is because 1-421/2 is not a real number.
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