7.2 Properties of Rational Exponents

Do properties of exponents work for roots?What form must they be in?

How do you know when a radical is in simplest form?

Before you can add or subtract radicals what must be true?

Everything you learned in Algebra I about exponents in one section to be applied to

rational exponents.

Properties of Rational Exponents

aaanmnm

aamnnm

baab mmm

0,1

a

aa m

m

0, aa

aa nm

n

m

0,

bba

ba

m

mm

554121

23121

58

4144

32

731

7

2

31

31

412

Using Properties of Radicals

Use the properties of radicals to simplify the expression

33 164

4

4

2

162

Write the expression in simplest form

3 54

5

4

3

Adding & Subtracting Roots and Radicals

665151

27

33 216

Simplify the expression involving variables

63 125y

21102

9 vu

4 8

4

yx

zy

x

x531

21

2

6

Write the expression in simplest form

5 13955 cba

3 7

yx

Add or subtract the expression involving variables.

yy 65

3131 72 xyxy

3 23 5 4053 xxx

• Do properties of exponents work for roots?Same rules apply.• What form must radical be in?Fractional exponent form• How do you know when a radical is in

simplest form?When there are no more perfect squares.• Before you can add or subtract radicals

what must be true?The number under the radicals must be the

same.

Assignment

p. 411, 24-78 (x3)