Chapter 8: Exercises with Answers

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 8.1 Exponents and Roots 765 Version: Fall 2007 8.1 Exercises In Exercises 1 - 12 , compute the exact value. 1. 3 - 5 2. 4 2 3. (3 / 2) 3 4. (2 / 3) 1 5. 6 - 2 6. 4 - 3 7. (2 / 3) - 3 8. (1 / 3) - 3 9. 7 1 10. (3 / 2) - 4 11. (5 / 6) 3 12. 3 2 In Exercises 13 - 24 , perform each of the following tasks for the given equation. i. Load the left- and right-hand sides of the given equation into Y1 and Y2 , re- spectively. Adjust the WINDOW para- meters until all points of intersection (if any) are visible in your viewing window. Use the intersect utility in the CALC menu to determine the coordinates of any points of intersec- tion. ii. Make a copy of the image in your viewing window on your homework paper. Label and scale each axis with Copyrighted material. See: 1 xmin, xmax, ymin, and ymax. Label each graph with its equation. Drop dashed vertical lines from each point of intersection to the x -axis, then shade and label each solution of the given equation on the x -axis. Remember to draw all lines with a ruler. iii. Solve each problem algebraically. Use a calculator to approximate any radi- cals and compare these solutions with those found in parts (i) and (ii). 13. x 2 = 5 14. x 2 = 7 15. x 2 = - 7 16. x 2 = - 3 17. x 3 = - 6 18. x 3 = - 4 19. x 4 = 4 20. x 4 = - 7 21. x 5 = 8 22. x 5 = 4 23. x 6 = - 5 24. x 6 = 9 In Exercises 25 - 40 , simplify the given radical expression. 25. 49 26. 121
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766 Chapter 8 Exponential and Logarithmic Functions Version: Fall 2007 27. - 36 28. - 100 29. 3 27 30. 3 - 1 31. 3 - 125 32. 3 64 33. 4 - 16 34. 4 81 35. 4 16 36. 4 - 625 37. 5 - 32 38. 5 243 39. 5 1024 40. 5 - 3125 41. Compare and contrast ( - 2) 2 and ( - 2) 2 . 42. Compare and contrast 4 ( - 3) 4 and ( 4 - 3) 4 . 43. Compare and contrast 3 ( - 5) 3 and ( 3 - 5) 3 . 44. Compare and contrast 5 ( - 2) 5 and ( 5 - 2) 5 . In Exercises 45 - 56 , compute the exact value. 45. 25 - 3 2 46. 16 - 5 4 47. 8 4 3 48. 625 - 3 4 49. 16 3 2 50. 64 2 3 51. 27 2 3 52. 625 3 4 53. 256 5 4 54. 4 - 3 2 55. 256 - 3 4 56. 81 - 5 4 In Exercises 57 - 64 , simplify the prod- uct, and write your answer in the form x r . 57. x 5 4 x 5 4 58. x 5 3 x - 5 4 59. x - 1 3 x 5 2 60. x - 3 5 x 3 2 61. x 4 5 x - 4 3 62. x - 5 4 x 1 2 63. x - 2 5 x - 3 2 64. x - 5 4 x 5 2 In Exercises 65 - 72 , simplify the quo- tient, and write your answer in the form x r . 65. x - 5 4 x 1 5
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Section 8.1 Exponents and Roots 767 Version: Fall 2007 66. x - 2 3 x 1 4 67. x - 1 2 x - 3 5 68. x - 5 2 x 2 5 69. x 3 5 x - 1 4 70. x 1 3 x - 1 2 71. x - 5 4 x 2 3 72. x 1 3 x 1 2 In Exercises 73 - 80 , simplify the expres- sion, and write your answer in the form x r . 73. x 1 2 4 3 74. x - 1 2 - 1 2 75. x - 5 4 1 2 76. x - 1 5 - 3 2 77. x - 1 2 3 2 78. x - 1 3 - 1 2 79. x 1 5 - 1 2 80. x 2 5 - 1 5
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768 Chapter 8 Exponential and Logarithmic Functions Version: Fall 2007 8.1 Answers 1. 1 243 3. 27 8 5. 1 36 7. 27 8 9. 7 11. 125 216 13. Solutions: x = ± 5 x - 10 10 y - 10 10 y = x 2 y =5 - 2 . 2361 2 . 2361 15. No real solutions. x - 10 10 y - 10 10 y = x 2 y = - 7 17. x = 3 - 6 x - 10 10 y - 10 10 y = x 3 y = - 6 - 1 . 8171
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Section 8.1 Exponents and Roots 769 Version: Fall 2007 19. Solutions: x = ± 4 4 x - 10 10 y - 10 10 y = x 4 y =4 - 1 . 4142 1 . 4142 21. x = 5 8 x - 10 10 y - 10 10 y = x 5 y =8 1 . 5157 23. No real solutions.
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