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Rational Exponents 10. 10. 2 2 1. Evaluate rational exponents. 2. Write radicals as expressions raised to rational exponents. 3. Simplify expressions with rational number exponents using the rules of exponents. 4. Use rational exponents to simplify radical expressions.

Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

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Page 1: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Rational Exponents10.210.2

1. Evaluate rational exponents.2. Write radicals as expressions raised to rational

exponents.3. Simplify expressions with rational number exponents

using the rules of exponents.4. Use rational exponents to simplify radical expressions.

Page 2: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

2505

25251

5

12

1

Integer ExponentsInteger Exponents

25

Page 3: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

32 xx 5x

32x

432ba 128ba

6x

Integer ExponentsInteger Exponents

Page 4: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

2/116 2/124

Rational ExponentsRational Exponents

2

12

4

441

2/125 2/125 2

12

5

551

3/18 3/132 31

32

221

16

25

3 8

New notation for a familiar concept!

Denominator is the index (root) of the radical.

Page 5: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

3/127 3273

Evaluate:Evaluate:

2/125 525

5/132 2325

3/1343 73433

Page 6: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

4/181 3814

Evaluate:Evaluate:

4/181

3/11000 1010003

3/18 283

Not a real number

3/18

21

81

81

33/1

4 81

Page 7: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

2/122a a22

Rewrite in Radical Notation:Rewrite in Radical Notation:

8/1w

2/13x 3 x

8 w

Page 8: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

2/34 32/14

Rational ExponentsRational Exponents

32 8

Numerator is the power.

2/34 2/134 2/164 8

ba

xpower

root

Generally easier to find the root first and then the power.

Page 9: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

3/227 92723

Evaluate:Evaluate:

2/325

4/581 2438154

3/227

91

27

127

1233/2

125253

Page 10: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

3/21000 100100023

Evaluate:Evaluate:

4/316

5/332 83235

5/31 1

81634

Page 11: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Slide 10- 11Copyright © 2011 Pearson Education, Inc.

Simplify.

a) 4

b)

c) 4

d)

2/38

1

4

1

4

Page 12: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Slide 10- 12Copyright © 2011 Pearson Education, Inc.

Simplify.

a) 4

b)

c) 4

d)

2/38

1

4

1

4

Page 13: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

8 33 8/133

Write in Exponential Form:Write in Exponential Form:

7 5r

7 3

5

n 7/3

5n

83 m 3/8m

7/5r

Page 14: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Rules of ExponentsRules of Exponents

32 xx 532 xx

2/13/2 nn 63

64

n2

1

3

2

n 6

1

n

Page 15: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Rules of ExponentsRules of Exponents

52 32 xx 76x

2/35/4 48 cc 1015

108

32

c2

3

5

4

32

c 10

23

32c

Page 16: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Rules of ExponentsRules of Exponents

2

5

xx

325 xx

2/1

8/5

xx 8

485

x21

85

x 81

x

Page 17: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Rules of ExponentsRules of Exponents

32x 632 xx

5/22/3m 53

m5

2

2

3

m

Page 18: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Simplify radical expressions:Simplify radical expressions:

4 36

4/136 4/126 41

12

6

21

6 62

1

Page 19: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Simplify radical expressions:Simplify radical expressions:

6 27

6/127 6/133 61

13

3

21

3 32

1

Page 20: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Simplify radical expressions:Simplify radical expressions:

10 82ba

10/182ba 10

18

10

12

ba 54

51

ba 51

4ab 5 4ab

Page 21: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Simplify radical expressions:Simplify radical expressions:

3 25 4 xx

3

2

5

4

xx 1510

1512

x 15

22

x 15 22x

Page 22: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Simplify radical expressions:Simplify radical expressions:

4 5 z

45

1

z4

1

5

1

z 20

1

z 20 z

Page 23: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Slide 10- 23Copyright © 2011 Pearson Education, Inc.

Simplify.

a)

b)

c)

d)

3/ 41/ 2 2 /3x y

3/8 1/ 4x y

3/8 3/ 4x y

3/8 1/ 2x y

3/ 4 1/ 2x y

Page 24: Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational

Slide 10- 24Copyright © 2011 Pearson Education, Inc.

Simplify.

a)

b)

c)

d)

3/ 41/ 2 2 /3x y

3/8 1/ 4x y

3/8 3/ 4x y

3/8 1/ 2x y

3/ 4 1/ 2x y