Properties of Exponents Examples and Practice. Product of Powers Property How many factors of x are in the product x 3 ∙x 2 ? Write the product as a single.

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Properties of Exponents

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Presentation transcript:

Properties of Exponents Examples and Practice

Product of Powers Property How many factors of x are in the product x 3 ∙x 2 ? Write the product as a single power. In general: 5 factors: x∙x∙x∙x∙x x∙x∙x∙x∙x = x 5 x m ∙x n = x m + n

Question #1 Simplify the expression: a 3  a 5 a. a 15 b. a 8 c. a 2 d. 1/a 2

Question #2 Simplify the expression: (3m 2 )  (2m 4 ) a. 6m 8 b. 5m 6 c. 5m 8 d. 6m 6

Question #3 Simplify the expression: (-2xy 3 )  (5x 4 y 2 ) a. -10x 5 y 5 b. -10x 4 y 5 c. 3x 5 y 5 d. -10x 4 y 6

Power of a Power Property How many factors of x are in the expression (x 3 ) 2? Write the product as a single power. In general: 6 factors: x 3 ∙ x 3 = x∙x∙x∙x∙x∙x (x∙x∙x)∙(x∙x∙x) = x 6 (x m ) n = x m∙n

Question #4 Simplify the expression: (4 2 ) 5 a. 4 7 b c d. 16 7

Question #5 Simplify the expression: (x 3 ) 4 a. x 7 b. 2x 7 c. x 12 d. 2x 12

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) = x 2 y 2 (x∙y) m = x m y m

Question #6 Simplify the expression: (b 3 c 2 ) 4 a. b 7 c 6 b. b 12 c 8 c. b 7 c 8 d. 2b 12 c 8

Question #7 Simplify the expression: (-3a 3 b) 2 a. 6a 5 b 2 b. 9a 5 b 2 c. -9a 6 b 2 d. 9a 6 b 2

Question #8 Simplify the expression: (-3a 3 b) 2 (2ab) a. 36a 7 b 3 b. 18a 7 b 3 c. -6a 7 b 3 d. -18a 7 b 3

Quotient of Powers Property Simplify the expression. In general:

Question #9 Simplify the expression: a. a 5 b. a 9 c. 1/a 5 d. 1/a 9

Question #10 Simplify the expression: a. a 5 b. 6 c. d.

Question #11 Simplify the expression: a. -3a 5 b. -16a 5 c. -3a 8 d. -16a 8

Question #12 Simplify the expression: a. b. c.d. 0.75a 4 b 3

Power of a Quotient Property Simplify the expression. In general:

Question #13 Simplify the expression: a. b. c.d. 0.2

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

Zero Exponent Property In general:

Question #15 Simplify the expression: x 0 y 2 a. b. xy 2 c. y 2 d.

Question #16 Simplify the expression: 2(3x 2 ) 0 a. 6x 2 b. 1 c. 6 d. 2

Question #17 Simplify the expression: (3x) 3 (5-x) 0 a. 3x 3 b. 15x 3 c. 27x 3 d. 15x 3 -5x 4

Negative Exponent Property a -m = ; a≠0 **Tip** To make an exponent positive change it’s location within in the base

Negative Exponents

Question #18

Question #19

Question #20