CHAPTER 7 Powers, Roots, and Scientific Notation

# 7.6 Chapter Review

# Review Exercises

## Simplify Expressions with Exponents

In the following exercises, simplify.

1. | 2. |

3. | 4. |

5. | 6. |

## Simplify Expressions Using the Product Property for Exponents

**In the following exercises, simplify each expression.
**

7. | 8. |

9. | 10. |

11. | 12. |

## Simplify Expressions Using the Power Property for Exponents

In the following exercises, simplify each expression.

13. | 14. |

15. | 16. |

## Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

17. | 18 |

19. | 20. |

## Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

21. | 22. |

23. | 24. |

25. | 26. |

## Simplify Expressions Using the Quotient Property for Exponents

In the following exercises, simplify.

27. | 28. |

29. | 30. |

31. | 32. |

## Simplify Expressions with Zero Exponents

In the following exercises, simplify.

33. | 34. |

35. | 36. |

37. | 38. |

39. | 40. |

## Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

41. | 42. |

43. | 44. |

## Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

45. | 46. |

47. | 48. |

49. | 50. |

51. | 52. |

## Divide Monomials

In the following exercises, divide the monomials.

53. | 54. ÷ |

55. | 56. |

## Use the Definition of a Negative Exponent

In the following exercises, simplify.

57. | 58. |

59. | 60. |

61. | 62. |

## Simplify Expressions with Integer Exponents

In the following exercises, simplify.

63. | 64. |

65. | 66. |

67. | 68. |

69. | 70. |

## Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

71. 0.00429 | 72. 8,500,000 |

73. In 2015, the population of the world was about 7,200,000,000 people. | 74. The thickness of a dime is about 0.053 inches. |

## Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

75. 1.5 × | 76. 3.8 × |

77. 5.5 × | 78. 9.1 × |

## Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

79. 3.5 ×(6.2 × | 80. 2 × (4 × |

In the following exercises, divide and write your answer in decimal form.

81. | 82. |

## Simplify Expressions with Square Roots

In the following exercises, simplify.

83.
85. 87. 89. |
84.
86. 88. 90. |

## Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

91. | 92. |

## Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

93. | 94. |

## Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

95.
97. 99. 101. |
96.
98. 100. 102. |

## Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

103.Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of square feet. How long can a side of the flower garden be?
105. |
104. Art Diego has square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?
106. |

# Review Exercise Answers

1. 17 | 3. 0.125 |

5. | 7. |

9. | 11. |

13. | 15. |

17. | 19. |

21. | 23. |

25. | 27. |

29. | 31. |

33. 1 | 35. 1 |

37. 1 | 39. 0 |

41. | 43. |

45. 1 | 47. |

49. | 51. |

53. | 55. |

57. | 59. |

61. | 63. |

65. | 67. |

69. | 71. |

73. | 75. |

77. | 79. |

81. | 83. 12 |

85. −9 | 87. not a real number |

89. 17 | 91. |

93. 7.55 | 95. 8b |

97. 15mn | 99. 7y |

101. 11cd | 103. 5.5 feet |

105. 72 mph |

# Practice Test

In the following exercises, simplify each expression.

1. | 2. |

3. | 4. |

5. | 6. |

7. | 8. |

9. | 10. |

11. | 12. |

13. | 14. |

15. | 16. |

17. | 18. |

19. | 20. |

21. Convert 83,000,000 to scientific notation. | 22. Convert to decimal form. |

# Practice Test Answers

1. | 2. |

3. | 4. |

5. | 6. |

7. | 8. |

9. | 10. |

11. | 12. |

13. | 14. |

15. 9 | 16. -7 |

17. not a real number | 18. |

19. | 20. |

21. | 22. 0.0000691 |