By Bernard Kolman; Arnold Shapiro

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50. xy 53. ( -�x3y-4r J 54. 2b-4 57. (a2a-3c58. 3r {a + b)b}- 21 62. 61 . (a -n n 65. (�) = (�) 1 2 . -3r3r3 1 6. -(2x2)S 20. (3;:r 24. [(3b + 1 )5 ]5 28. � (y4)6 32. (xy)o 36. x- s (2a) -6 (x-2)4 48. - 1 0 x l x •2 7 ( - 2rc-2)n (x2)3(y2)4(x3)7 {-2ab2b)4 (-3a 2)3 3 ( -�a2b3c2) (-3) -3 -x- s 4y5y-2 [ (x + y) - 2]2 (x4y -2) (x-2-2)2J (3y ) ix- 3y2 x- ly- 3 (a- 1 + b- 1 ) - 1 I Show that [ill]- 68. 6s5-2· r Consider a square whose area is length a. 462 Ifill. 69. 46- 1 rl square centimeters, and whose sides are of a2 = 25 so that a is a number whose square is 25.

38. 37. (-x)3 42. 41 . 5 - 355 45. (x- J) - J 46. y 4 2 2x2 -J 49. 50. xy 53. ( -�x3y-4r J 54. 2b-4 57. (a2a-3c58. 3r {a + b)b}- 21 62. 61 . (a -n n 65. (�) = (�) 1 2 . -3r3r3 1 6. -(2x2)S 20. (3;:r 24. [(3b + 1 )5 ]5 28. � (y4)6 32. (xy)o 36. x- s (2a) -6 (x-2)4 48. - 1 0 x l x •2 7 ( - 2rc-2)n (x2)3(y2)4(x3)7 {-2ab2b)4 (-3a 2)3 3 ( -�a2b3c2) (-3) -3 -x- s 4y5y-2 [ (x + y) - 2]2 (x4y -2) (x-2-2)2J (3y ) ix- 3y2 x- ly- 3 (a- 1 + b- 1 ) - 1 I Show that [ill]- 68. 6s5-2· r Consider a square whose area is length a.

26. It 27. � 25. � 28. %7 30 . JR) 31. � 29. v(-5)2 32. In Exercises 34-36 provide a real value for each variable to demonstrate the result. 35. Yx2 + y2 x + y 36. Vx vY vry 34. W x In Exercises 37-56 write the expression in simplified form. (Every variable represents a positive real number. ) 38. v'200 39. €4 40. v? 37. v4s 42. � 43. � 41. V7 44. VxY 46. v24b wc 14 47. � 45. Yx9 48. Y20x5y7z4 4 l 50. 3Vil 51. V3y 49. � 52. /y 2b2 4x2 54. 28av'2b 55. vrxy 53. v'h 56. �48x8y6z2 In Exercises 57-66 simplify and combine terms .