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exposé - matière potentielle : journey historyP a g e | 1 Institute of Education Travel, Subsistence and Other Expenses Policy December 2011claims for reimbursement of expenses by individuals breakfast accommodation ioe business mileage rate institute expenses travel staff cost time time time after time time to time

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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 y6 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 n Simplify .  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 y1xy =  Group powers with the same base.  22 44x1     1 13(2) = (x) Quotient of Powers and Negative Exponent Properties  8 4y    5 1x1 =   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 12  21  1 =(x)(y)   2   10 01 =x yor  2 2   The answer is C.

Substitute.

Quotient of Powers

0 0 x= 1 andy= 1

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