Properties of Rational Exponents

Section 7.2

WHAT YOU WILL LEARN:1. Simplify expressions with rational exponents.

2. Use properties of rational exponents.

3. Write an expression involving rational exponents in simplest form.

4. Perform operations with rational exponents.

5. Simplify expressions that have variables and rational exponents.

6. Write an expression involving variables and rational exponents in simplest form.

7. Perform operations with rational exponents and variables.

Properties of Rational Exponents

nmnm aaa

Properties of Rational Exponents:

Property: Example:

1.

2. (am)n = amn

3. (ab)m = ambm

4.

93333 2)2

3

2

1(

2

3

2

1

6444)4( 3)22

3(22

3

62349)49( 2

1

2

1

2

1

0,1

aa

am

m

5

1

25

125

2

12

1

Properties of Rational Exponents (cont.)

0, aaa

a nmn

m

Properties of Rational Exponents:

Property: Example:

5.

6.

3666

6

6 2)2

1

2

5(

2

1

2

5

0,)( ab

a

b

am

mm

3

2

27

8)

27

8(

3

1

3

1

3

1

Using the Properties

4

1

2

1

55

• Simplify the expressions:

1.

2.

3.

23

1

2

1

)58(

4

144 )32(

More Fun with Properties

3

1

7

74.

5. 2

3

1

3

1

)

4

12(

You Try

3

4

1

4

1

3

2

3

133

24

1

3

1

3

1

2

1

9

18

6

6

)24(

)627(

66

• Simplify:

1.

2.

3.

4.

5.

More Simplifying

33 164

• Simplify the expressions:

1.

2.

4

4

2

162

You Try

33 525

• Simplify:

1.

2. 3

3

4

32

Simplest Form - continued

3 54

• In order for a radical to be in simplest form, you have to remove any perfect nth powers and rationalize denominators. Example:

Write in simplest form:

1. 2. 5

4

3

You Try

4

4

8

7

64

• Write in simplest form:

1.

2.

Operations Using Radicals

)6(2)6(7 5

1

5

1

• Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example:

• Perform the indicated operation:

1. 2. 33 216

You Try

33

4

3

4

3

381

)4(3)4(5

• Perform the indicated operation:

1.

2.

Simplifying Expressions Involving Variables

nn x

• Important!

= x when n is odd.

= |x| when n is even.

nn x

Simplifying

3 6125y

• Simplify the expression. Assume all variables are positive:

1. 2.

3. 4.

2

1102 )9( vu

48

4

y

x53

1

2

1

2

6

zx

xy

You Try

34

1

3

2

410

5

2

124

3 9

6

18

)16(

27

tr

rs

y

x

hg

z

• Simplify the expression. Assume all variables are positive.

1.

2.

3.

4.

Writing Variable Expressions in Simplest Form

5 13955 cba

• Write the expression in simplest form. Assume all variables are positive.

1. 2. 37y

x

You Try

57

2

4 149412

h

g

fed

• Write the expression in simplest form. Assume all variables are positive.

1.

2.

Adding and Subtracting Expressions Involving Variables

yy 65

• Perform the indicated operation. Assume all variables are positive.

1. 2.

3.

3

1

3

1

72 xyxy

3 23 5 4053 xxx

You Try

44 5

4

1

4

1

662

63

38

xxx

ghgh

xx

• Perform the indicated operations. Assume all variables are positive.

1.

2.

3.

Homework

page 411, 22-30 even, 34-62 even, 66-72 even, 76, 80

: