ANSWERS TO YOU TRY EXERCISES 1) a) base: 5; exponent: 3; 53 125 b) base: 8; exponent: 2; 82 64 c) base: 2 3 ; exponent: 3; a 2 3 b 3 8 27 2) a) 27 b) y14 c) 54m16 d) h14 e) 1323 3) a) 512 b) j30 c) 64 4) a) k28 b) 64k60m18 c) r6s24 d) 36t2u2 5) a) 25 144 b) 32 d 5 c) u6 v6 10.1 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Evaluate Exponential Expressions Rewrite each expression using exponents. 1) 9 9 9 9 9 9 96 2) 4 4 4 4 4 4 4 47 3) a1 7 ba1 7 ba1 7 ba1 7 b a1 7 b 4 4) (0.8)(0.8)(0.8) (0.8)3 5) (5)(5)(5)(5)(5)(5)(5) (5)7 6) (c)(c)(c)(c)(c) (c)5 7) (3y)(3y)(3y)(3y)(3y)(3y)(3y)(3y) 8) a 5 4 tba 5 4 tba 5 4 tba 5 4 tb a 5 4 tb 4 Identify the base and the exponent in each. 9) 68 base: 6; exponent: 8 10) 94 base: 9; exponent: 4 11) (0.05)7 12) (0.3)10 13) (8)5 14) (7)6 15) (9x)8 16) (13k)3 17) (11a)2 18) (2w)9 19) 5p4 base: p; exponent: 4 20) 3m5 base: m; exponent: 5 21) 3 8 y2 base: y; exponent: 2 22) 5 9 t7 base: t; exponent: 7 23) Evaluate (3 4)2 and 32 42. Are they equivalent? Why or why not? 24) Evaluate (7 3)2 and 72 32. Are they equivalent? Why or why not? 25) For any values of a and b, does (a b)2 a2 b2? Why or why not? Answers may vary. 26) Does 24 (2)4? Why or why not? 27) Are 3t4 and (3t)4 equivalent? Why or why not? (3y)8 base: 0.05; exponent: 7 base: 0.3; exponent: 10 base: 8; exponent: 5 base: 7; exponent: 6 base: 9x; exponent: 8 base: 13k; exponent: 3 base: 11a; exponent: 2 base: 2w; exponent: 9 No, 3t4 3 t4; (3t)4 34 t4 81t4 28) Is there any value of a for which (a)2 a2? Support your answer with an example. Evaluate. 29) 25 32 30) 92 81 31) (11)2 121 32) 43 64 33) (2)4 16 34) (5)3 125 35) 34 81 36) 62 36 37) 23 8 38) 82 64 39) a1 5 b 3 1 125 40) a3 2 b 4 81 16 For Exercises 41–44, answer always, sometimes, or never. 41) Raising a negative base to an even exponent power will always, sometimes, or never give a negative result. 42) If the base of an exponential expression is 1, the result will always, sometimes, or never be 1. always 43) If b is any integer value except zero, then the exponential expression (b)3 will always, sometimes, or never give a negative result. sometimes 44) If a is any integer value except zero, then the exponential expression a4 will always, sometimes, or never give a positive result. never Objective 2: Use the Product Rule for Exponents Evaluate the expression using the product rule, where applicable. 45) 22 23 32 46) 52 5 125 47) 32 32 81 48) 23 23 64 49) 52 23 200 50) 43 32 576 51) a1 2 b 4 a1 2 b 2 1 64 52) a4 3 b a4 3 b 2 64 27 Yes. If a 0, then (0)2 0 and 02 0. never 774 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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