Aim: How do we work on the expression with fractional exponent?

Do Now: Simplify:

1. 22

2. 33 22

3.33 22

2

8

HW: p.297 # 20,26,32,44,48,50,54,64,66,68

3 4

If we write as then becomes2 2

1

2 22

2

1

2

1

22 2

1

2

1

2

221

22222 2

1

2

1

8222222 32

6

2

3

2

333

In the same fashion,

333 422 or 3

2

3

1

3

133 22222

Law of Fractional ExponentLaw of Fractional Exponent:

nn xx 1

n an

a

xx

ann

a

xx )(

ann

an

a

xx

x)(

11

33

1

xx

3 23

2

xx

233

2

xx

3 23

23

2 11

xx

x

Evaluating in Either Order

46488

4288

33 23

2

223

3

2

or

Evaluating a-m/n

4

1

2

1

8

1

8

18 22

33

23

2

4

3

81

4

3

81

1

34 )81(

1

27

1

3

13

Simplifying

abba

yyy

3

1

2

1

6

16

6

16

13

11

2

1 ba

3

2

2

3

ba

1.

2.

or 3 23 ba

2. 274

3

Examples:

273 4

1. 363

2

3 4

81

36 3 6 3

216

3. 813

4 814 3 3 3

27

Examples: rewrite the expression with positive exponent

xy 1

8

21

2

1

4 22

4

1

4 21

4

Examples: Simplify each expression

32

1

10

41

8

25

1

10

22 1

8

2

5

10

22

8

2

1

2

21

4

3210

48

24

Examples: Simplify each expression

5

1

2

251

2

5 1

2

2 5

125

1

2

51

2

125

1

2

1

2

125 1

1215

110

Express as a rational number:

1. 3

5

8

2. 2

1

9

3. 2

3

100

Write the following as a power with positive exponent

1. 3 15

2. 6418 ba

3.b

a

4

3

Write the following as a radical expression

1. 2

1

5

2. 2

12 )25( yx

3. 41

6516 ba