1. Objectives Simplify quotients of powers. Simplify powers of fractions. Page 383 – Laws of Exponents: Dividing Monomials

2. Glossary Terms Power-of-a-Fraction Property Quotient-of-Powers Property

3. Rules and Properties Quotient-of-Powers Property For all nonzero real numbers x and all integers m and n, where m > n, = x m – n xmxm xnxn When you divide two numbers with the same base, subtract the exponents

4. Simplify 26242624 = 2 6-4 =2² = 4 10 9 10² = 10 9-2 = 10 7 =10,000,000 x a x = x a-1 x a+b x c = x a+b+-c x m+1 x = x m+1-1 = xmxm

5. Quotients of Monomials To find quotients of monomials, treat the coefficients separately, and use the Quotients-of-Powers Property to simplify powers with the same base. -4x²y 5 2xy³ = -4 2 · x 2-1 · y 5-3 = -2xy² c 4 b c²a = c 4-2 · abab = c²a b

6. Rules and Properties Power-of-a-Fraction Property For all real numbers a, b, and n, where n  0 and b  0 anan bnbn a b n () = Again, the exponent goes with everything in the numerator and the denominator. Examples page 386

7. Key Skills Use the properties of exponents to simplify expressions containing fractions. a. 15x 7 y 3 3xy 2 Use the Quotient-of-Powers Property. 15 5  x 7 – 1  y 3 – 2 = = 3x 6 y

8. Key Skills Use the properties of exponents to simplify expressions containing fractions. Use the Power-of-a-Fraction Property. b. 3w3z3w3z k2k2 ( ) 2 (3w 3 z) 2 (k2)2(k2)2 = 9w6z29w6z2 k4k4 = TOC

9. Assignment Page 387 – 389 –18 –64 even, 82, 84, 85, 87