SECTION A.10 nth Roots; Rational Exponents A93 Skill Building In Problems 11–54, simplify each expression. Assume that all variables are positive when they appear. 11. 27 3 12. 16 4 13. 8 3 − 14. 1 3 − 15. 8 16. 75 17. 700 18. x 45 3 19. 32 3 20. 54 3 21. x8 4 3 − 22. x 192 5 3 23. 243 4 24. x 48 5 4 25. x y 4 12 8 26. x y 5 10 5 27. x y xy 9 7 3 4 28. xy x y 3 81 2 4 2 3 29. x 64 30. x9 5 31. x y 162 9 12 4 32. x y 40 14 10 3 − 33. x x 15 5 2 34. x x 5 20 3 35. 5 9 3 2 ( ) 36. 3 10 3 4 ( ) 37. 3 6 2 2 ( )( ) 38. 5 8 3 3 ( )( ) − 39. 3 2 4 2 + 40. 6 5 4 5 − 41. 48 5 12 − + 42. 2 12 3 27 − 43. 3 3 3 1 ( )( ) + − 44. 5 2 5 3 ( )( ) − + 45. 5 2 2 54 3 3 − 46. 9 24 81 3 3 − 47. x 1 2 ( ) − 48. x 5 2 ( ) + 49. x x 16 2 4 3 3 − 50. x x 32 2 4 4 5 + 51. x x 8 3 50 3 − 52. x y y 3 9 4 25 + 53. x y x xy xy 16 3 2 5 2 4 3 3 4 3 − + − 54. xy x y x y 8 25 8 2 2 3 3 3 − + 3. In the symbol a, n the integer n is called the . 4. We call a 3 the of a . 5. Multiple Choice Let n 2 ≥ and m 2 ≥ be integers, and let a and b be real numbers. Which of the following is not a property of radicals? Assume all radicals are defined. (a) a b a b n n n = (b) a b a b n n n + = + (c) ab a b n n n = (d) a a n m n m ( ) = 6. Multiple Choice If a is a real number and n 2 ≥ is an integer, then which of the following expressions is equivalent to a, n provided that it exists? (a) a n− (b) an (c) a 1 n (d) a n 1/ 7. Multiple Choice Which of the following phrases best defines like radicals? (a) Radical expressions that have the same index (b) Radical expressions that have the same radicand (c) Radical expressions that have the same index and the same radicand (d) Radical expressions that have the same variable 8. Multiple Choice To rationalize the denominator of the expression 2 1 3 , − multiply both the numerator and the denominator by which of the following? (a) 3 (b) 2 (c) 1 3 + (d) 1 3 − 9. True or False 32 2 5 − = − 10. True or False 3 3 4 4 ( ) − = − Concepts and Vocabulary In Problems 55–68, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 55. 1 2 56. 2 3 57. 3 5 − 58. 3 8 − 59. 3 5 2 − 60. 2 7 2 + 61. 2 5 2 3 5 − + 62. 3 1 2 3 3 − + 63. 5 2 1 − 64. 3 5 4 − + 65. 5 2 3 66. 2 9 3 − 67. x h x x h x + − + + 68. x h x h x h x h + + − + − − A.10 Assess Your Understanding ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages in red. 1. 3 2 ( ) − = ; 3 2 − = (pp. A7–A9) 2. 16 = ; 4 2 ( ) − = (pp. A9–A10) 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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