1. Exponents

2. 1. Relate and apply the concept of exponents (incl. zero). 2. Perform calculations following proper order of operations. 3. Applying laws of exponents to compute with integers. 4. Naming square roots of perfect squares through 225.

3. EXPONENT LAWS

4. Basic Terminology BASE EXPONENT means

5. 0²=0 6²=36 12²=144 1²=1 7²=49 13²=169 2²=4 8²=64 15²=225 3²=9 9²=81 16²=256 4²=16 10²=100 20²=400 5²=25 11²=121 25²=625

6. Write the following expression using an exponent: 2·2·2·2·2·2

7. Answer: 2⁶

8. Simplify the following problems completely. Your answer should not contain exponents. 3³

9. Answer: 27

10. Simplify the following problems completely. Your answer should not contain exponents. Example: 2³·2² = 2⁵ = 32 Are you ready? 3, 2, 1…lets go!

11. (-4)³

12. Answer: -64

13. (-2)³

14. Answer: -8

15. (-2)⁴

16. Answer: 16

17. (-2)⁵

18. Answer: -32

19. Important! * If a negative number is raised to an even number power, the answer is positive. * If a negative number is raised to an odd number power, the answer is negative.

20. (-2)²

21. Answer: 4

22. (-12)²

23. Answer: 144

24. -3²

25. Answer: -9

26. Warning!!! The missing parenthesis makes all the difference. The square of a negative & the negative of a square are not the same thing! Example: (-2)² ≠ -2²

27. IMPORTANT EXAMPLES

28. Exponent Rule: a ∙ aⁿ = a m + nm Example2: 2³ ∙ 2² = 2³⁺² = 2⁵ = 32 Example1: 2 ∙ 2 = 2¹⁺¹ = 2² = 4

29. Are you ready? 3, 2, 1…lets go!

30. Simplify. Your answer should contain only positive exponents. 2 · 2² · 2²

31. Answer: 2⁵

32. Simplify. Your answer should contain only positive exponents. 4² · 4²

33. Answer: 4⁴

34. Simplify. Your answer should contain only positive exponents. 4 · 4²

35. Answer: 4³

36. Simplify. Your answer should contain only positive exponents. 3² · 3²

37. Answer: 3⁴

38. Simplify Completely. Your answer should not contain exponents. 3⁵ · 3¯⁵

39. Answer: 1

40. (-1) + 1 (5²) (2⁵) Simplify Completely. Your answer should not contain exponents.

41. Answer: 0

42. Exponent Rule: (a )ⁿ = a Example: ( 2² )⁵ = 2 = 2¹⁰ = 1,024 m m · n 2·5

43. Contest Problem Are you ready? 3, 2, 1…lets go!

44. Simplify. Your answer should contain only positive exponents. (2³)³

45. Answer: 2⁹

46. Simplify. Express your answer with a base of 2 and an exponent. Example: 2² (8)³

47. Answer: 2⁹

48. Simplify. Express your answer with a base of 2 and an exponent. Example: 2² 4² · 4²

49. Answer: 2⁸

50. Simplify. Express your answer with a base of 2 and an exponent. Example: 2² 4 · 4²

51. Answer: 2⁶

52. Exponent Rule: (ab)² = a²b² Example: (4·6)² = 4²·6²

53. Simplify Completely. Your answer should not contain exponents. 5³ · 2³

54. Answer: 1000

55. Simplify Completely. Your answer should not contain exponents. (5·4)³

56. Answer: 8000

57. Exponent Rule: a ÷aⁿ = a m - nm Example: 2⁵ ÷ 2² = 2⁵¯² = 2³ = 8

58. Problems Are you ready? 3, 2, 1…lets go!

59. Evaluate Completely: 5⁴ 5

60. Answer: 125

61. Evaluate Completely: 2² 2³

62. Answer: 1/2

63. Exponent Rule: (1/a)² = 1/a² Example: (1/7)² = 1/7² = 1/49

64. Simplify. (1/4)³

65. Answer: 1/64

66. Exponent Rule: (a/b)² = a²/b² Example: (7/12)² = 7²/12² = 49/144

67. Exponent Rule: (a÷b)ⁿ = aⁿ÷bⁿ = aⁿ/bⁿ Example: (2÷5)³ = (2÷5)·(2÷5)·(2÷5) = (―)·(―)·(―) =(2·2·2)/(5·5·5) =2³/5³ = 8/125 2525 2525 2525

68. Problems Are you ready? 3, 2, 1…lets go!

69. Simplify. (2/3)³

70. Answer: 8/27

71. Exponent Rule: a⁰ = 1 Examples: ( 17 )⁰ = 1 ( 99 )⁰ = 1

72. Exponent Rule: (a)¯ⁿ = 1÷aⁿ Example: 2¯⁵ = 1 ÷ 2⁵ = 1/32

73. Problems Are you ready? 3, 2, 1…lets go!

74. (2)¯³

75. Answer: 1/8

76. (-2)¯³

77. Answer: - 1/8

78. -2 ⁽¯⁴⁾

79. Answer: - 1/16

80. (2) ¯³ · (-16)

81. Answer: -2

82. 56 · (2)¯³

83. Answer: 7

84. 56 ÷ (2)¯³

85. Answer: 448

86. 1 ÷ (-3)¯²

87. Answer: 9

88. Exponents in Order of Operations 1) Parenthesis →2) Exponents 3) Multiply & Divide 4) Add & Subtract

93. Exponents & Order of Operations

94. Contest Problems Are you ready? 3, 2, 1…lets go!

95. -6 - (-4)(-5) - (-6)

96. Answer: -20

97. 180 – 5 · 2²

98. Answer: 160

99. -3 - (1)¯⁵

100. Answer: -4

101. 8 ( 6² - 3(11) ) ÷ 8 + 3

102. Answer: 6

103. ( 2² )³ · (6 – 7)² - 2·3² ÷ 6

104. Answer: 61

105. 2 ( 10² + 3 · 18 ) ÷ ( 5² ÷ 2¯² )

106. Answer: 3.08