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. Accident investigation The skid marks of a car involved in an accident were feet. How fast had the car been going before applying the brakes? |
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. Gravity A hiker dropped a granola bar from a lookout spot feet above a valley. How long did it take the granola bar to reach the valley floor? |
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 |