By Cynthia Y. Young

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2 # 14 7 3 61. 4b a , 9 27 65. 3x 9 , 4 16y a Z 0 y Z 0 58. 2# 9 3 10 62. 3a b , 7 21 66. 14m # 4 2 7 b Z 0 59. 2 10 , 7 3 63. 3x 6x , 10 15 x Z 0 64. 4 1 1 , 7 5 20 67. 3y 6x , 7 28 y Z 0 68. 2 1# 5 7 3 6 In Exercises 69–72, evaluate the algebraic expression for the speciﬁed values. 69. 71. ■ -c 2d for c ϭ Ϫ4, d ϭ 3 m1 # m2 r 2 for m1 ϭ 3, m2 ϭ 4, r ϭ 10 70. 2l ϩ 2w 72. x - m s for for l ϭ 5, w ϭ 10 x ϭ 100, m ϭ 70, s ϭ 15 A P P L I C AT I O N S On December 16, 2007, the United States debt was estimated at $9,176,366,494,947, and at that time the estimated population was 303,818,361 citizens.

2 Ϫ 3[(4x Ϫ 5) Ϫ 3x Ϫ 7] - 14 5 - (- 2) -3 (5)(- 1) 32. - 35. Ϫ(6x Ϫ 4y) Ϫ (3x ϩ 5y) 39. - 4(5) - 5 -5 36. 12 (-3)(-4) -4x 6 - (- 2) 40. Ϫ6(2x ϩ 3y) Ϫ [3x Ϫ (2 Ϫ 5y)] In Exercises 41–56, write as a single fraction and simplify. 41. 1 5 + 3 4 42. 1 1 2 5 43. 5 1 6 3 44. 7 1 3 6 45. 3 5 + 2 12 46. 1 5 + 3 9 47. 1 2 9 27 48. (-4) 3 5 7 3 6 49. x 2x + 5 15 50. y y 3 6 51. x 2x 3 7 52. y y 10 15 53. 4y (- 3y) 15 4 54. 6x 7x 12 20 55. 3 7 + 40 24 56. -3 -7 - a b 10 12 60. 4 7 , 5 10 In Exercises 57–68, perform the indicated operation and simplify, if possible.

2)3 # 52 = (-2)(-2)(-2) # 5 # 5 = Evaluate the expression Ϫ43 # 23. So far, we have discussed only exponents that are natural numbers (positive integers). When the exponent is a negative integer, we use the following property. N E GATIVE - I NTE G E R ■ Answer: Ϫ512 Study Tip A negative exponent implies a reciprocal. E X P O N E NT P R O P E RT Y Let a be any nonzero real number and n be a natural number (positive integer); then a-n = 1 an a Z 0 In other words, a base raised to a negative-integer exponent is equivalent to the reciprocal of the base raised to the opposite (positive) integer exponent.