1. Exponents

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

3. EXPONENT LAWS

4. Basic Terminology
EXPONENT
means
BASE

5. IMPORTANT EXAMPLES

6. Variable Expressions

7. Substitution and Evaluating
STEPS
Write out the original problem.
Show the substitution with parentheses.
Work out the problem.
= 64

8. Evaluate the variable expression when x = 1, y = 2, and w = -3
Step 1
Step 1
Step 1
Step 2
Step 2
Step 2
Step 3
Step 3
Step 3

9. MULTIPLICATION PROPERTIES
PRODUCT OF POWERS
This property is used to combine 2 or more exponential expressions with the SAME base.

10. MULTIPLICATION PROPERTIES
POWER TO A POWER
This property is used to write and exponential expression as a single power of the base.

11. MULTIPLICATION PROPERTIES
POWER OF PRODUCT
This property combines the first 2 multiplication properties to simplify exponential expressions.

12. MULTIPLICATION PROPERTIES
SUMMARY
PRODUCT OF POWERS
ADD THE EXPONENTS
POWER TO A POWER
MULTIPLY THE EXPONENTS
POWER OF PRODUCT

13. ZERO AND NEGATIVE EXPONENTS
ANYTHING TO THE ZERO POWER IS 1.

14. DIVISION PROPERTIES QUOTIENT OF POWERS
This property is used when dividing two or more exponential expressions with the same base.

15. DIVISION PROPERTIES
POWER OF A QUOTIENT
Hard Example

16. ZERO, NEGATIVE, AND DIVISION PROPERTIES
Zero power
Quotient of powers
Negative Exponents
Power of a quotient

17. 0²= ²= ²=144 1²= ²= ²=169 2²= ²= ²=225 3²= ²= ²=256 4²= ²= ²=400 5²= ²= ²=625

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

19. Exponents & Order of Operations

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

21. 180 – 5 · 2²

22. Answer: 160

23. Evaluate the expression when y= -3 (2y + 5)²

24. Answer: 1

25. -3²

26. Answer: -9

27. Warning. The missing parenthesis makes all the difference
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

28. Contest Problems

29. Are you ready? 3, 2, 1…lets go!

30. 8(6² - 3(11)) ÷ 8 + 3

31. Answer: 6

32. Evaluate the expression when a= -2 a² + 2a - 6

33. Answer: -6

34. Evaluate the expression when x= -4 and t=2 x²(x-t)

35. Answer: -96

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

37. Simplify (in terms of 2 to some power)
Simplify (in terms of 2 to some power). Your answer should contain only positive exponents. 4² · 4²

38. Answer: 2⁸

39. Simplify (in terms of 2 to some power)
Simplify (in terms of 2 to some power). Your answer should contain only positive exponents · 2² · 2²

40. Answer: 2⁵

41. Simplify. Your answer should contain only positive exponents
Simplify. Your answer should contain only positive exponents. 2n⁴ · 5n ⁴

42. Answer: 10n⁸

43. Simplify. Your answer should contain only positive exponents. 6r · 5r²

44. Answer: 30r³

45. Simplify. Your answer should contain only positive exponents. 6x · 2x²

46. Answer: 12x³

47. Simplify. Your answer should contain only positive exponents
Simplify. Your answer should contain only positive exponents. 6x² · 6x³y⁴

48. Answer: 36x⁵y⁴

49. Simplify. Your answer should contain only positive exponents
Simplify. Your answer should contain only positive exponents. 10xy³ · 8x⁵y³

50. Answer: 80x⁶y⁶

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

52. Answer: 1

53. (-4)³

54. Answer: -64

55. (-2)⁴

56. Answer: 16

57. 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.

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

59. (5²) (2⁵)
(-1)

60. Answer: 0

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

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

63. 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 2 5 2 5 2 5

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

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

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

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

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

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

70. Simplify. Your answer should contain only positive exponents. 5⁴ 5

71. Answer: 5³ (125)

72. Simplify. Your answer should contain only positive exponents. 2² 2³

73. Answer: 1/2

74. Simplify. Your answer should contain only positive exponents. 3r³ 2r

75. Answer: 3r² 2

76. Simplify. Your answer should contain only positive exponents. 3xy 5x²2 ( )

77. Answer: 9y² 25x²

78. Simplify. Your answer should contain only positive exponents
Simplify. Your answer should contain only positive exponents. 18x⁸y⁸ 10x³

79. Answer: 9x⁵y⁸ 5

80. Simplify. Your answer should contain only positive exponents. (a²)³

81. Answer: a⁶

82. Simplify. Your answer should contain only positive exponents. (3a²)³

83. Answer: 27a⁶

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

85. Answer: 2⁹

86. Simplify. Your answer should contain only positive exponents. (8)³

87. Answer: 2⁹

88. Simplify. Your answer should contain only positive exponents. (x⁴y⁴)³

89. Answer: x¹²y¹²

90. Simplify. Your answer should contain only positive exponents. (2x⁴y⁴)³

91. Answer: 8x¹²y¹²

92. Simplify. Your answer should contain only positive exponents. (4x⁴∙x⁴)³

93. Answer: 64x²⁴

94. Simplify. Your answer should contain only positive exponents. (4n⁴∙n)²

95. Answer: 16n¹⁰

96. Simplify the following problems completely
Simplify the following problems completely. Your answer should not contain exponents. Example: 2³·2² = 2⁵ = 32

97. -3 - (1)¯⁵

98. Answer: -4

99. (2)¯³

100. Answer: 1/8

101. (-2)¯³

102. Answer: - 1/8

103. -2⁽¯⁴⁾

104. Answer: - 1/16

105. (2)¯³ · (-16)

106. Answer: -2

107. 56 · (2)¯³

108. Answer: 7

109. 56 ÷ (2)¯³

110. Answer: 448

111. 1 ÷ (-3)¯²

112. Answer: 9

113. (2²)³ · (6 – 7)² - 2·3² ÷ 6

114. Answer: 61

115. -6 - (-4)(-5) - (-6)

116. Answer: -20

117. 2 (10² + 3 · 18) ÷ (5² ÷ 2¯²)

118. Answer: 3.08

119. Simplify: (x⁴y¯²)(x¯¹y⁵)

120. Answer: x³y³

121. Competition Problems Points: 1 minute: 5 points 1 ½ minute: 3 points 2 minute: 1 point 3, 2, 1, … go!

122. Simplify: (4x4y)3 (2xy3)

123. Answer: 128x13y6

124. If A = (7 – 11 + 8)131 and B = (–7 + 11 – 8)131 then what is the value of: (7 – 13)(A+B)

125. Answer: 1

126. Simplify:

127. Answer:

128. Evaluate for x = –2, y = 3 and z = –4:

129. Answer: -540

130. If A♣B = (3A–B)3, then what is (2♣8)♣6?

131. Answer: -27,000

132. If a*b is defined as (ab)2 + 2b, and x y is defined as xy2 - 2y, find 2*(3 4).

133. Answer: 6480

134. Simplify: 24 – 4(12 – 32 – 60)

135. Answer: 16

136. If x = the GCF of 16, 20, and 72 and y = the LCM of 16, 20, and 72, what is xy?

137. Answer: 2880

138. Express in simplest form:

139. Answer:

140. Simplify:

141. Answer: 32

142. Simplify. Write the answer with negative exponents. (abc)-3c2b a-4bc2a

143. Answer: b-3c-3

144. Simplify …

145. Answer: 1/900

146. Solve for n:

147. Answer: n = 2/3

148. .
Solve for q:

149. Answer: no solution

150. .
Simplify:

151. Answer: