10.3: rational exponents

April 27, 2009

Objectives

1. Define rational exponents2. Simplify expressions that contain rational

exponents3. Estimate the value of an expression using a

calculator4. Write expressions in radical or exponential

form, interchangeably

Rational numbers as exponents• Rational numbers are also called:• Consider:

a = 91/2

what would you do to both sides?(a)2=(91/2)2

a2 = 9a=3

So…3=91/2

Fractions!

Rules for rational exponents

a1/n = n√aam/n = n√am

Remember these previously discussed rules:am *an = am+n

am /an = am-n

(am)n = am*n

(ab)m = am*bm

(a/b)m = am/bm

Write in radical form, then simplify

251/2

271/3

93/2

(16/81)3/4

(-8)2/3

16-1/2

27-2/3

Additional rules

x2/3 * x1/2

x3/4

x1/2

(x2/3)3/4

Even trickier

(x2/3*y5/6)3/2

Write in radical form

a3/5

(mn)3/4

2y5/6

(2y)5/6

Write in exponential form

3√(5x)

√(9a2b4)

4√(16w12z8)

Your assignment

• p. 695-696#14-76even