Properties of Exponents Examples and Practice Product of

Properties of Exponents Examples and Practice

Product of Powers Property • How many factors of x are in the product x 3∙x 2? 5 factors: x∙x∙x • Write the product as a single power. x∙x∙x = x 5 • In general: xm∙xn= xm + 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: (3 m 2) (2 m 4) a. 6 m 8 b. 5 m 6 c. 5 m 8 d. 6 m 6

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

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 (x 3)2? 6 factors: x∙x∙x∙x • Write the product as a single power. (x∙x∙x)∙(x∙x∙x) = x 6 • In general: (xm)n= xm∙n

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

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

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

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. 2 b 12 c 8

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

Question #8 • Simplify the expression: (-3 a 3 b)2(2 ab) a. 36 a 7 b 3 b. 18 a 7 b 3 c. -6 a 7 b 3 d. -18 a 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. 1/a 5 d. 1/6

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

Question #12 • Simplify the expression: a. b. c. d. 0. 75 a 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. c. y 2 d. xy 2