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Lesson 82 Example 1Quotient of Powers 3 6 2 6x y Simplify .Assume thatxandyare not equal to zero. 4 6x y 3 6 23 62 6x y6 y=Group powers that have the same base.4 4 6x y6y     3  16  42  1  =(6 )(x)(y)Quotient of Powers2 22  =6x yor 36x ySimplify.Example 2 Power of a Quotient 2 2 3m nSimplify . 5p 2 2 2 2 (3m n) 3m n=Power of a Quotient 2 5p (5p)   2 2 2 2 (3)(m)n =Power of a Product2 2 5p 4 2 9m n =Power of a Power2 25p Example 3Zero Exponent Simplify each expression. Assume that no denominator is equal to zero. 2 30 a. (0.6a b) 2 300 (0.6a b1) =a= 12 x y b. 0 x 2 2 x yx y0 =a= 10 1 2 =x ySimplify.
Example 4 Negative Exponents Simplify each expression. Assume that no denominator is equal to zero. 38 x y a. 2 4x 38 38 x y1xy=  Group powers with the same base.  22 44x1     113(2) = (x) Quotient of Powers and Negative Exponent Properties  8 4y    5 1x1=   Simplify.8 41y     5 x =Multiply fractions.8 4y 32 3 (2c d) b. 46 9c d 32 33 96 (2c d)2c d =Power of a Product4646 9c d9c d 8 9 –(4) 6– (6)3 = (c)(d)= 8Quotient of Powers, 29 8 13 0 = c dSimplify.9 13 8c = Zero Exponent Properties and Multiply9 Example 5Apply Properties of Exponents MultipleChoice Test Item Write the ratio of the height of the triangle to the base of the triangle in simplest form. 1 11 A B CD2 4 2 Read the Test Item A ratio is a comparison of two quantities. It can be written in fraction form. Solve the Test Item 2 the height of the triangle isx y 2 the base of the triangle is 2x y
2 height of trianglex y = base of triangle 2 2x y 12  21  1  =(x)(y)   2   10 01  =x yor  2 2   The answer is C.
Substitute.
Quotient of Powers
0 0 x= 1 andy= 1