Properties of Exponents Examples and Practice

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

Question #1 Simplify the expression: a3a5 a. a15 b. a8 c. a2 d. 1/a2

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

Question #3 Simplify the expression: (-2xy3)(5x4y2) a. -10x5y5 b. -10x4y5 c. 3x5y5 d. -10x4y6

Negative exponents are improper To convert, take the reciprocal of the base and make the exponent positive

Simplify the following:  

Simplify the following:  

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

Question #4 Simplify the expression: (42)5 a. 47 b. 1610 c. 410 d. 167

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

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

Question #6 Simplify the expression: (b3c2)4 a. b7c6 b. b12c8 c. b7c8 d. 2b12c8

Question #7 Simplify the expression: (-3a3b)2 a. 6a5b2 b. 9a5b2 c. -9a6b2 d. 9a6b2

Question #8 Simplify the expression: (-3a3b)2(2ab) a. 36a7b3 b. 18a7b3 c. -6a7b3 d. -18a7b3

Quotient of Powers Property Simplify the expression. In general:

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

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

Question #11 Simplify the expression: a. -3a5 b. -16a5 c. -3a8 d. -16a8

Question #12 Simplify the expression: a. b. c. d. 0.75a4b3

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: x0y2 a. b. xy2 c. y2 d.