1

How Do We Use Rational Exponents?

• Do Now: Perform the indicated operation and simplify

1.

2.

2

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

3

Square Root of x2

Page 393

xx 2

4

Radicals

5

Rational Exponents

6

Exponent 1/n When n Is Even

7

When n Is Even

definedyetnotis44

26464

5625625

10100100

2

1

66

1

44

1

2

1

8

Exponent 1/n When n Is Odd

9

Exponent 1/n When n Is Odd

2

1

32

1

32

1

32727

32727

55

1

33

1

33

1

10

nth Root of Zero

00 n

11

Rational Exponents

12

Evaluating in Either Order

46488

4288

33 23

2

223

3

2

or

13

Negative Rational Exponents

14

Evaluating a-m/n

4

1

2

1

8

1

8

18 22

33

23

2

15

Rules for Rational Exponents

7-6

16

Simplifying

abba

yyy

3

1

2

1

6 66

16

17

Simplifying

3

2

2

3

13

11

2

1

113

1

2

1

3

1

2

1

6 66

16

ba

ba

babaabba

yyy

18

Simplifying

2

112108

3

2

2

3

3

1

2

1

6 66

16

9 zyx

baabba

yyy

19

Multiplying Radicals – Different Indices

32

82222222

3

44 34

3

2

1

4

1

2

1

4

14

20

Multiplying RadicalsDifferent Indices

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

3232

82222222

21

Different Indices

6

3

6

2

2

1

3

13

44 34

3

2

1

4

1

2

1

4

14

323232

82222222

22

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

23

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

24

Rational ExponentsEliminate the root, then the power

23

2

a

25

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

26

Negative Exponents

11 3

2

r

27

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

28

Negative ExponentsEliminate the root, then the power

132 3

2

t

29

No SolutionEliminate the root, then the power

132

132

132

132

2

2

33

3

2

3

2

t

t

t

t

30

No SolutionEliminate the root, then the power

solutionrealNo

t

t

t

t

132

132

132

132

2

2

33

3

2

3

2

31

Strategy for Solving Equations with Exponents and Radicals

32

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