3 32 n5 n7 n57 n2 10.2 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Mixed Exercises: Objectives 1 and 2 Determine whether each statement is true or false. 1) 80 1 true 2) Raising a positive base to a negative exponent will give a negative result. (Example: 24) false 3) 60 40 (6 4)0 4) 32 22 12 false Evaluate each expression. Assume that the variables do not equal zero. 5) 20 1 6) (4)0 1 7) 50 1 8) 10 1 9) r0 1 10) (5m)0 1 11) 2k0 2 12) z0 1 13) (5)0 (5)0 2 14) a4 7 b 0 a7 4 b 0 0 15) a7 8 b 0 a3 5 b 0 0 16) x0 (2x)0 2 17) 62 1 36 18) 92 1 81 19) 24 1 16 20) 112 1 121 21) 53 1 125 22) 25 1 32 EXAMPLE 4 In-Class Example 4 Simplify using the quotient rule, if possible. Assume that the variables do not equal zero. a) 74 72 b) n12 n4 c) 2 23 d) x3 x5 e) 23 92 Answer: a) 49 b) n8 c) 16 d) 1 x 2 e) 8 81 Simplify using the quotient rule, if possible. Assume that the variables do not equal zero. a) 29 23 b) t10 t4 c) 3 32 d) n5 n7 e) 32 24 Solution a) 29 23 293 26 64 The bases are the same, so subtract the exponents. b) t10 t4 t104 t6 Because the bases are the same, subtract the exponents. c) 31 32 31(2) The bases are the same, so subtract the exponents. 33 27 Be careful when subtracting the negative exponent! d) 1 n2 Same base; subtract the exponents. Write with a positive exponent. e) 32 24 9 16 Because the bases are not the same, we cannot apply the quotient rule. Evaluate the numerator and denominator separately. YOU TRY 4 Simplify using the quotient rule, if possible. Assume that the variables do not equal zero. a) 57 54 b) c4 c1 c) k2 k10 d) 23 27 e) 62 53 Be careful when you subtract exponents, especially when you are working with negative numbers! ANSWERS TO YOU TRY EXERCISES 1) a) 1 b) 1 c) 1 d) 2 e) 1 f) 8 g) 1 h) 2 2) a) 1 100 b) 1 125 c) 1 m4 3) 7 50 4) a) 125 b) c5 c) 1 k8 d) 210 e) 36 125 false www.mhhe.com/messersmith SECTION 10.2 Integer Exponents and the Quotient Rule 779
messersmith_power_prealgebra_1e_ch4_7_10
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