Section 7 2 Apply Exponent Properties Involving Quotients

Section 7 -2 Apply Exponent Properties Involving Quotients

Section 7. 1 REVIEW, “Apply Exponent Properties Involving Products” (1) Product of Powers Property (2) Power of a Power Property (3) Power of a Product Property

Section 7. 2, “Apply Exponent Properties Involving Quotients” (1) Quotient of Powers Property (2) Power of a Quotient Property

Quotient of Powers Property ● To divide powers having the same base, SUBTRACT the exponents. Example: 47 = 47 - 2 = 45 42 Power of a Quotient Property ● To find a power of a quotient, find the power of the numerator and the power of the denominator and DIVIDE. Example: 3 7 = 37 2 27

Division of Powers: Can think of division of powers as the following if confused: a 5 = a • a • a 2 = a a 3 a • a

Example 1 Use the quotient of powers property: 1. 912 = 912 - 5 = 97 95 2. (-2)4 = (-2)4 - 3 =(-2)1 = -2 (-2)3 3. 63 64 • 62 3 + 4 = 67 = 7 - 2 6 6 = 65 = 62 62 r 8 4. 1 • r 8 = = 5 5 r r 1 r 8 -5 3 r =

Example 2 Use the power of a quotient property: 1. c 6 = c 6 d d 6 2. -2 y 4 = (-2)4 =16 y 4

Example 3 Use properties of exponents: 33 • a 4 • 3 1. 3 a 4 3= = 5 b 53 • b 3 2. x 3 y 7 • 1 3 x 8 27 a 12 125 b 3 3 • 7 • 21 = x 1 x = = 3 x 8 y 7 8 13 y 7 3 x x 21 – 8 x = 7 3 y

Try It Out. . . (1) Quotient of Powers Property

Try It Out. . . (2) Power of a Quotient Property

Try It Out. . . Use All Properties of Exponents