7.2 1

7.2 Rational Exponents Rational Exponents Exponential Expressions – Variables in Bases Rational Exponents with Numerators > 1 Negative Rational Exponents Applying Exponent Rules Simplifying Radical Expressions

7.2 2

Rational (Fractional) Exponents Rational Exponents can be used to express

and manipulate factors containing radicals

21

51

31

99776464 53

7.2 3

Recall the Rules for Integer Exponents

5555 exponents, of rule theUsing

555555 expression that theseecan We

122

122

1

2

835 xxx 1535 )( aa 216372 )( yxyx

6

10

3

5 2

ba

ba

10 y3

13

xx 2

4

6

xxx 33

5

3

3

5

ab

ba

7.2 4

Practice

71

31

21

)4(4)3(3)44(44 723 2 zzyyxx

42)2()2(1616 244 21

21

21

Express using rational exponents:

Simplify using rational exponents:

2

3

2

3

8

27

8

273

1

31 3

3

7.2 5

Expressions with Variable BasesAssume that all variables are unrestricted and use

absolute value symbols when necessary.

If we are told that the variables represent positive real numbers, the absolute value symbol in the answer for the first problem is not needed.

aaaaa 5)5()5())5(()625( 1)4

1(4

4144

14

2)2

1(4)

2

1(2

21422

14 55)5()25( bbbb

7.2 6

Summary

5)5(

533

1

31

00

0

41

41

7))7((

)7(33

1

31

#

)7( 61

realanot

7.2 7

Rational Expressions Where the Numerator is greater than 1

644161616 3322 32

3

6422216 62342

342

3

Using Exponent Arithmetic, it’s a little easier

7.2 8

Negative Rational Exponents

125

1

5

1

5

1

25

125

32 23

23

23

23

3

9

1

)3(

127

32

32

aaa

7.2 9

Using Rational Exponents to Simplify Radicals

Simplify

xyyx

yxyxyx

2222

2)2(64

21

21

21

21

21

23

412264 22

7.2 10

Examples

27

8

3

2

3

2

9

432 2

323

22333 9)3(27 32

32

baabba

44

2

6

3

6 16

9

)2(

3

)2(

3

64

2732

32

32

yyyy

7.2 11

Examples

66293

9

4

1

)2(

1

2

18

32

32

zzzz

125

343

5

7

5

7

25

49

49

253

3

2

2

23

23

23

23

7.2 12

What Next? Starring:

7.3 Multiplying Radical Expressions