Rational exponents

1

2

3

How Do We Use Rational Exponents?

• Do Now: Perform the indicated operation and simplify

1.

2.

4

nth Rootsnth Roots

An nth root of number a is a number whose nth power is a.

a number whose nth power is a

If the index n is even, then the radicand a must be nonnegative.

is not a real number

n a

4 4

5

16 2, 16

32 2

but

5

Square Root of x2

Page 393

xx 2

6

Radicals

7

Rational Exponents

8

Exponent 1/n When n Is Even

9

When n Is Even

definedyetnotis44

26464

5625625

10100100

2

1

66

1

44

1

2

1

10

Exponent 1/n When n Is Odd

11

Exponent 1/n When n Is Odd

2

1

32

1

32

1

32727

32727

55

1

33

1

33

1

12

nth Root of Zero

00 n

13

Rational Exponents

14

Evaluating in Either Order

46488

4288

33 23

2

223

3

2

or

15

Negative Rational Exponents

16

Evaluating a-m/n

4

1

2

1

8

1

8

18 22

33

23

2

17

Rules for Rational Exponents

7-6

18

Simplifying

abba

yyy

3

1

2

1

6 66

16

19

Simplifying

3

2

2

3

13

11

2

1

113

1

2

1

3

1

2

1

6 66

16

ba

ba

babaabba

yyy

20

Simplifying

2

112108

3

2

2

3

3

1

2

1

6 66

16

9 zyx

baabba

yyy

21

Multiplying Radicals – Different Indices

32

82222222

3

44 34

3

2

1

4

1

2

1

4

14

22

Multiplying RadicalsDifferent Indices

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

3232

82222222

23

Different Indices

6

3

6

2

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

323232

82222222

24

Different Indices

6 36 26

3

6

2

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

32323232

82222222

25

Different Indices

66 36 26

3

6

2

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

10832323232

82222222

26

Rational ExponentsEliminate the root, then the power

23

2

a

27

Eliminate the Root, Then the Power

CHECK

a

a

a

a

a

22

8

8

2

2

2

2

3

3

3

2

3

2

28

Negative Exponents

11 3

2

r

29

Negative ExponentsEliminate the root, then the power

CHECK

rr

r

r

r

r

r

02

11

11

11

11

11

2

2

33

3

2

3

2

30

Negative ExponentsEliminate the root, then the power

132 3

2

t

31

No SolutionEliminate the root, then the power

132

132

132

132

2

2

33

3

2

3

2

t

t

t

t

32

No SolutionEliminate the root, then the power

solutionrealNo

t

t

t

t

132

132

132

132

2

2

33

3

2

3

2

33

Strategy for Solving Equations with Exponents and Radicals