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Mathematics LibreTexts

0.02e: Exercises - Whole number exponents

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A: Zero and Negative Exponents

Exercise 0.2.1

  Simplify. (Assume all variables represent nonzero numbers.)

1.    5x0

2.    3x2y0

3.    2x3

4.    (2x)2

5.    10x3y2

6.    3x5y2

7.    3x2y2z1

8.    5x4y2z2

Answers to odd exercises.
1. 5 3. 2x3 5. 10y2x3 7. 3y2x2z

B: Product Rule

Exercise 0.2.2

  Simplify. (Assume all variables represent nonzero numbers.)

11.    104107

12.    7372

13.    x3x2

14.    y5y3

15.    a4a5a2

16.    b8b3b4

17.    5x2y3xy2

18.    10x3y22xy

19.    6x2yz33xyz4

20.    2xyz2(4x2y2z)

21.    3xny2n5x2y

22.    8x5nyn2x2ny

23.    (2x+3)4(2x+3)9

24.    (3y1)7(3y1)2

25.    (a+b)3(a+b)5

26.    (x2y)7(x2y)3

Answers to odd exercises.

11. 1011

13. x5

15. a

17. 15x3y3

19. 18x3y2z7

21. 15xn+2y2n+1

23. (2x+3)13

25. (a+b)8

C: Quotient Rule

Exercise 0.2.3

  Simplify. (Assume all variables represent nonzero numbers.)

31.    102104105

32.    757972

33.    a8a6a5

34.    b4b10b8

35.    a8a3a6

36.    b10b4b2

37.    25x3y25x1y3

38.    9x1y3z53x2y2z1

39.    40x5y3z4x2y2z

40.    8x2y5z316x2yz

41.    24a8b3(a5b)108a5b3(a5b)2

42.    175m9n5(m+n)725m8n(m+n)3

43.    x2nx3nxn

44.    xnx8nx3n 

Answers to odd exercises.

31. 10

33. a9

35. a11

37. 5y5x2

39. 10x3y

41. 3a3(a5b)8

43. x4n

D: Power Rule for Products

Exercise 0.2.4

  Simplify. (Assume all variables represent nonzero numbers.)

51.    (x5)3

52.    (y4)3

53.    (x4y5)3

54.    (x7y)5

55.    (5x)0

56.    (3x2y)0

57.    (x2y3z4)4

58.    (xy2z3)2

59.    (5x2yz3)2

60.    (2xy3z4)5

61.    (xx3x2)3

62.    (y2y5y)2

63.    (2x4y2z)6

64.    (3xy4z7)5

65.    (2a2b0c3)5

66.    (3a4b2c0)4

67.    (5x3y2z)3

68.    (7x2y5z2)2

69.    (x2yz5)n

70.    (xy2z3)2n

71.    a2(a4)2a3

72.    aa3a2(a2)3

73.    (9x3y2z0)23xy2

74.    (5x0y5z)325y2z0

Answers to odd exercises.

51. x15

53. x12y15

55. 1

57. x8y12z16

59. 25x4y2z6

61. x18

63. 64x24y12z6

65. 32a10c15

67. x9125y6z3

69. x2nynz5n

71. a7

73. 27x5y2

E: Power Rule for Quotients of Products

Exercise 0.2.5 

  Simplify. (Assume all variables represent nonzero numbers.)  

81.    (3ab22c3)3

82.    (10a3b3c2)2

83.    (2xy4z3)4

84.    (7x9yz4)3

85.    (12x3y2z2x7yz8)3

86.    (150xy8z290x7y2z)2

87.    (2x3zy2)5

88.    (5x5z22y3)3

89.    (xy2z3)n

90.    (2x2y3z)n

91.    (9a3b4c23a3b5c7)4

92.    (15a7b5c83a6b2c3)3

Answers to odd exercises:

81. 27a3b68c9

83. 16x4y16z12

85. 216y3x12z21

87. x15y1032z5

89. xny2nz3n

91. a24b481c20


0.02e: Exercises - Whole number exponents is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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0.02: Review - whole number exponents
0.03: Review - Radicals (Square Roots)