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8.7 Review Exercises and Sample Exam

Review Exercises

(Assume all variables represent nonnegative numbers.)

Simplify.

1. $36$

2. $425$

3. $−16$

4. $−9$

5. $1253$

6. $3 −83$

7. $1643$

8. $−5 −273$

9. $40$

10. $−350$

11. $9881$

12. $1121$

13. $5 1923$

14. $2 −543$

Simplify.

15. $49x2$

16. $25a2b2$

17. $75x3y2$

18. $200m4n3$

19. $18x325y2$

20. $108x349y4$

21. $216x33$

22. $−125x6y33$

23. $27a7b5c33$

24. $120x9y43$

Use the distance formula to calculate the distance between the given two points.

25. (5, −8) and (2, −10)

26. (−7, −1) and (−6, 1)

27. (−10, −1) and (0, −5)

28. (5, −1) and (−2, −2)

Simplify.

29. $83+33$

30. $1210−210$

31. $143+52−53−62$

32. $22ab−5ab+7ab−2ab$

33. $7x−(3x+2y)$

34. $(8yx−7xy)−(5xy−12yx)$

35. $45+12−20−75$

36. $24−32+54−232$

37. $23x2+45x−x27+20x$

38. $56a2b+8a2b2−224a2b−a18b2$

39. $5y4x2y−(x16y3−29x2y3)$

40. $(2b9a2c−3a16b2c)−(64a2b2c−9ba2c)$

41. $216x3−125xy3−8x3$

42. $128x33−2x⋅543+3 2x33$

43. $8x3y3−2x⋅8y3+27x3y3+x⋅y3$

44. $27a3b3−3 8ab33+a⋅64b3−b⋅a3$

Multiply.

45. $3⋅6$

46. $(35)2$

47. $2(3−6)$

48. $(2−6)2$

49. $(1−5)(1+5)$

50. $(23+5)(32−25)$

51. $2a23⋅4a3$

52. $25a2b3⋅5a2b23$

Divide.

53. $724$

54. $104864$

55. $98x4y236x2$

56. $81x6y738y33$

Rationalize the denominator.

57. $27$

58. $63$

59. $142x$

60. $1215$

61. $12x23$

62. $5a2b5ab23$

63. $13−2$

64. $2−62+6$

Rational Exponents

65. $71/2$

66. $32/3$

67. $x4/5$

68. $y−3/4$

Write as a radical and then simplify.

69. $41/2$

70. $501/2$

71. $42/3$

72. $811/3$

73. $(14)3/2$

74. $(1216)−1/3$

Perform the operations and simplify. Leave answers in exponential form.

75. $31/2⋅33/2$

76. $21/2⋅21/3$

77. $43/241/2$

78. $93/491/4$

79. $(36x4y2)1/2$

80. $(8x6y9)1/3$

81. $( a 4/3 a 1/2)2/5$

82. $(16 x 4/3 y 2)1/2$

Solve.

83. $x=5$

84. $2x−1=3$

85. $x−8+2=5$

86. $3x−5−1=11$

87. $5x−3=2x+15$

88. $8x−15=x$

89. $x+41=x−1$

90. $7−3x=x−3$

91. $2(x+1)=2(x+1)$

92. $x(x+6)=4$

93. $x(3x+10)3=2$

94. $2x2−x3+4=5$

95. $3(x+4)(x+1)3=5x+373$

96. $3x2−9x+243=(x+2)23$

97. $y1/2−3=0$

98. $y1/3+3=0$

99. $(x−5)1/2−2=0$

100. $(2x−1)1/3−5=0$

Sample Exam

In problems 1–18, assume all variables represent nonnegative numbers.

1. Simplify.

1. $100$
2. $−100$
3. $−100$

2. Simplify.

1. $273$
2. $−273$
3. $−273$

3. $12825$

4. $1921253$

5. $512x2y3z$

6. $250x2y3z53$

Perform the operations.

7. $524−108+96−327$

8. $38x2y−(x200y−18x2y)$

9. $2ab(32a−b)$

10. $(x−2y)2$

Rationalize the denominator.

11. $102x$

12. $14xy23$

13. $1x+5$

14. $2−32+3$

Perform the operations and simplify. Leave answers in exponential form.

15. $22/3⋅21/6$

16. $104/5101/3$

17. $(121a4b2)1/2$

18. $(9 y 1/3 x 6)1/2y1/6$

Solve.

19. $x−7=0$

20. $3x+5=1$

21. $2x−1+2=x$

22. $31−10x=x−4$

23. $(2x+1)(3x+2)=3(2x+1)$

24. $x(2x−15)3=3$

25. The period, T, of a pendulum in seconds is given the formula $T=2πL32$, where L represents the length in feet. Calculate the length of a pendulum if the period is 1½ seconds. Round off to the nearest tenth.

1: 6

3: Not a real number

5: $5$

7: 1/4

9: $210$

11: $729$

13: $20 33$

15: $7x$

17: $5xy3x$

19: $3x2x5y$

21: $6x$

23: $3a2bc⋅ab23$

25: $13$

27: $229$

29: $113$

31: $93−2$

33: $4x−2y$

35: $5−33$

37: $−x3+55x$

39: $12xyy$

41: $4 x3−5 xy3$

43: $2x⋅y3$

45: $32$

47: $6−23$

49: −4

51: $2a$

53: $32$

55: $7xy26$

57: $277$

59: $72xx$

61: $4x32x$

63: $3+2$

65: $7$

67: $x45$

69: 2

71: $2 23$

73: 1/8

75: 9

77: 4

79: $6x2y$

81: $a1/3$

83: 25

85: 17

87: 6

89: 8

91: −1/2, −1

93: 2/3, −4

95: −5, 5/3

97: 9

99: 9

1:

1. 10
2. Not a real number
3. −10

3: $825$

5: $10xy3yz$

7: $146−153$

9: $6a2b−2ba$

11: $52xx$

13: $x−5x−25$

15: $25/6$

17: $11a2b$

19: 49

21: 5

23: −1/2, 1/3

25: 1.8 feet