1. EXAMPLE 3 Simplify expressions a. b –4 b 6 b 7 Product of powers property b.b. r –2 –3 s3s3 ( r – 2 ) –3 ( s 3 ) –3 = Power of a quotient property = r 6 s –9 Power of a power property = r 6 s 9 Negative exponent property c. 16m 4 n –5 2n –5 = 8m 4 n – 5 – (–5) Quotient of powers property = 8m 4 n 0 = 8m 4 Zero exponent property = b –4 + 6 + 7 = b 9

2. EXAMPLE 4 Standardized Test Practice SOLUTION (x –3 y 3 ) 2 x5y6x5y6 = (x –3 ) 2 (y 3 ) 2 x5y6x5y6 x –6 y 6 x5y6x5y6 = Power of a product property Power of a power property

3. EXAMPLE 4 = x – 6 – 5 y 6 – 6 Quotient of powers property = x –11 y 0 Simplify exponents. Zero exponent property = 1 x 11 Negative exponent property = x –11 1 The correct answer is B. ANSWER Standardized Test Practice

4. EXAMPLE 5 Compare real-life volumes Betelgeuse is one of the stars found in the constellation Orion. Its radius is about 1500 times the radius of the sun. How many times as great as the sun’s volume is Betelgeuse’s volume? Astronomy

5. EXAMPLE 5 SOLUTION Let r represent the sun’s radius. Then 1500r represents Betelgeuse’s radius. Betelgeuse’s volume Sun’s volume = 4 3 π (1500r) 3 4 3 π r3π r3 The volume of a sphere is πr 3. 4 3 = 4 3 π 1500 3 r 3 4 3 π r3 π r3 Power of a product property Compare real-life volumes

6. EXAMPLE 5 Zero exponent property = 3,375,000,000 Evaluate power. = 1500 3 1 = 1500 3 r 0 Quotient of powers property Compare real-life volumes Betelgeuse’s volume is about 3.4 billion times as great as the sun’s volume. ANSWER

7. GUIDED PRACTICE for Examples 3, 4, and 5 Simplify the expression. Tell which properties of exponents you used. 5. x –6 x 5 x 3 SOLUTION x –6 x 5 x 3 = x –6 x 5 + 3 Power of a product property = x 2 Simplify exponents.

8. GUIDED PRACTICE for Examples 3, 4, and 5 6. (7y 2 z 5 )(y –4 z –1 ) SOLUTION (7y 2 z 5 )(y –4 z –1 ) = (7y 2 z 5 )(y –4 z –1 ) = (7y 2 – 4 )(z 5 +(–1) ) = (7y –2 )(z 4 ) = 7z 4 y2y2 Power of a product property Simplify Negative exponent property

9. GUIDED PRACTICE for Examples 3, 4, and 5 7. s 3 2 t –4 s 3 2 t –4 (t –4 ) 2 s (3)2 = SOLUTION t –8 s6s6 = s6t8s6t8 = Power of a product property Evaluate power. Negative exponent property

10. GUIDED PRACTICE for Examples 3, 4, and 5 8. x 4 y –2 3 x3y6x3y6 x3y6x3y6 SOLUTION = (x 4 ) 3 (y –2 ) 3 (x 3 ) 3 (y 6 ) 3 Power of a powers property = x 12 y –6 x 9 y 18 Power of a powers property = x 3 y –24 Power of a Quotient property x 3 y 24 = Negative exponent property