Objectives

• Simplify quotients of powers.

• Simplify powers of fractions.

Page 383 – Laws of Exponents:Dividing Monomials

Glossary Terms

Power-of-a-Fraction Property

Quotient-of-Powers Property

Rules and Properties

Quotient-of-Powers Property

For all nonzero real numbers x and all integers m and n, where m > n,

= xm – nxm

xn

When you divide two numbers with the same base, subtract the exponents

Simplify26

24= 26-4 = 2² = 4

109

10²= 109-2 = 107 = 10,000,000

xa

x= xa-1

xa+b

xc= xa+b+-c

xm+1

x= xm+1-1 = xm

Quotients of MonomialsTo find quotients of monomials, treat the coefficients separately, and use the Quotients-of-Powers Property to simplify powers with the same base.

-4x²y5

2xy³= -4

2· x2-1 · y5-3 = -2xy²

c4bc²a

= c4-2 · ab

= c²a b

Rules and Properties

Power-of-a-Fraction Property

For all real numbers a, b, and n, where n 0 and b 0 an

bn

a

b

n( ) =

Again, the exponent goes with everything in the numerator and the denominator.

Examples page 386

Key SkillsUse the properties of exponents to simplify expressions containing fractions.

a.15x7y3

3xy2

Use the Quotient-of-Powers Property.

15

5 x7 – 1 y3 – 2= = 3x6y

Key SkillsUse the properties of exponents to simplify expressions containing fractions.

Use the Power-of-a-Fraction Property.

b.3w3z

k2( )2

(3w3z)2

(k2)2=

9w6z2

k4=

TOC

Assignment

• Page 387 – 389– 18 –64 even, 82, 84, 85, 87