Simplify the expression using the product rule. Leave your answer in exponential form. 53) 83 89 812 54) 64 63 67 55) 52 54 55 511 56) 124 12 122 127 57) (7)2 (7)3 (7)3 58) (3)5 (3) (3)6 59) b2 b4 b6 60) x4 x3 x7 61) k k2 k3 k6 62) n6 n5 n2 n13 63) 8y3 y2 8y5 64) 10c8 c2 c 10c11 65) (9m4)(6m11) 54m15 66) (10p8)(3p) 30p9 67) (6r)(7r4) 42r5 68) (8h5)(5h2) 40h7 69) (7t6)(t3)(4t7) 28t16 70) (3k2)(4k5)(2k4) 24k11 71) Does the product rule apply to 3x2 4x2? Why or (7)8 (3)12 why not? Evaluate the expression. No. 3x2 4x2 is the sum of two terms. 3x2 4x2 7x2 72) Does the product rule apply to 5c3 7c3? Why or why not? Evaluate the expression. No. 5c3 7c3 is the difference of two terms. 5c3 7c3 2c3 73) Evaluate. a) 8p5 2p5 b) (8p5)(2p5) 16p10 6p5 74) Evaluate. a) 9k4 3k4 b) (9k4)(3k4) 27k8 12k4 Mixed Exercises: Objectives 3–5 Simplify the expression using one of the power rules. 75) (y3)4 y12 76) (x5)8 x40 77) (w11)7 w77 78) (a3)2 a6 79) (33)2 729 80) (22)2 16 81) ((5)3)2 (5)6 82) ((4)5)3 (4)15 83) a1 3 b 4 1 81 84) a5 2 b 3 125 8 85) a6 a b 2 36 a2 86) a v 4 b 3 v3 64 87) am n b 5 m5 n5 88) a t u b 12 t12 u12 89) (10y)4 10,000y4 90) (7w)2 49w2 91) (3p)4 81p4 92) (2m)5 32m5 93) (4ab)3 64a3b3 94) (2cd)4 16c4d4 95) 6(xy)3 6x3y3 96) 8(mn)5 8m5n5 97) 9(tu)4 9t4u4 98) 2(ab)6 2a6b6 99) (2w3)4 16w12 100) (3p8)2 9p16 101) (5m2n4)3 125m6n12 102) (2c9d 4)5 32c45d20 Mixed Exercises: Objectives 2–5 103) Find the area and perimeter of each rectangle. a) 3w w A 3w2 sq units; P 8w units b) 5k3 A 5k5 sq units; k2 P 10k3 2k2 units 104) Find the area. x x 52 5 4 x2 sq units R3) When do you add the exponents? R4) When do you multiply the exponents? R5) Which exercises in this section do you fi nd most challenging? Where could you go for help? R1) When can you “distribute” an exponent into parentheses? R2) When can you not “distribute” an exponent into parentheses? www.mhhe.com/messersmith SECTION 10.1 The Product Rule and Power Rules 775
messersmith_power_prealgebra_1e_ch4_7_10
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