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**Properties of Exponents**

Examples and Practice

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**Product of Powers Property**

How many factors of x are in the product x3∙x2? Write the product as a single power. In general: 5 factors: x∙x∙x∙x∙x x∙x∙x∙x∙x = x5 xm∙xn= xm + n

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Question #1 Simplify the expression: a3a5 a. a15 b. a8 c. a2 d. 1/a2

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**Question #2 Simplify the expression: (3m2)(2m4) a. 6m8 b. 5m6**

c. 5m8 d. 6m6

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**Question #3 Simplify the expression: (-2xy3)(5x4y2)**

a. -10x5y5 b. -10x4y5 c. 3x5y5 d. -10x4y6

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**Power of a Power Property**

How many factors of x are in the expression (x3)2? Write the product as a single power. In general: 6 factors: x∙x∙x∙x∙x∙x (x∙x∙x)∙(x∙x∙x) = x6 (xm)n= xm∙n

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Question #4 Simplify the expression: (42)5 a b c d. 167

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Question #5 Simplify the expression: (x3)4 a. x7 b. 2x7 c. x12 d. 2x12

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**Power of a Product Property**

How many factors of x and y are in the expression (xy)2? Simplify the expression. In general: 2 factors of each: (x∙y)∙(x∙y) (x∙y)∙(x∙y) = x2y2 (x∙y)m= xmym

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**Question #6 Simplify the expression: (b3c2)4 a. b7c6 b. b12c8**

c. b7c8 d. 2b12c8

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**Question #7 Simplify the expression: (-3a3b)2 a. 6a5b2 b. 9a5b2**

c. -9a6b2 d. 9a6b2

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**Question #8 Simplify the expression: (-3a3b)2(2ab) a. 36a7b3 b. 18a7b3**

c. -6a7b3 d. -18a7b3

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**Quotient of Powers Property**

Simplify the expression. In general:

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Question #9 Simplify the expression: a. a5 b. a9 c. 1/a5 d. 1/a9

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Question #10 Simplify the expression: a. a5 b. 6 c. 1/a5 d. 1/6

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**Question #11 Simplify the expression: a. -3a5 b. -16a5**

c. -3a8 d. -16a8

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Question #12 Simplify the expression: a. b. c. d a4b3

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**Power of a Quotient Property**

Simplify the expression. In general:

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Question #13 Simplify the expression: a. b. c. d

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Question #14 Simplify the expression: a. b. c. d.

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**Negative Exponent Property**

In general:

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**Question #15 Simplify the expression: (34)(3-2) a. 38 b. 3-8**

c d. 32

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Question #16 Simplify the expression: a. b. c. d.

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Question #17 Simplify the expression: a b. 26 c d.

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Question #18 Simplify the expression: a. b. c. d.

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Question #19 Simplify the expression: a. b. c. d.

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**Zero Exponent Property**

In general:

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Question #20 Simplify the expression: x0y-2 a. b. xy2 c. y2 d.

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