Rational (fraction) Rational (fraction) ExponentsExponents

Please READ as well as take Please READ as well as take notes & complete the notes & complete the

problems followed in these problems followed in these slides.slides.

Radical expression and Exponents

By definition of Radical Expression.

The index of the Radical is 3.

51251255 33 so

How would we simplify this expression?

What does the fraction exponent do to the number?

The number can be written as a Radical expression, with an index of the denominator.

21

9

2 9

The Rule for Rational Exponents

46464 331

1

nn bb

Write in Radical form

21

61

m

a

Write in Radical form

mm

aa

21

661

Write each Radical using Rational Exponents

w

b5

Write each Radical using Rational Exponents

21

51

5

ww

bb

What about Negative exponents

Negative exponents make inverses.

71

49

14921

21

What if the numerator is not 1

Evaluate5 25

2

3232

What if the numerator is not 1

Evaluate

5 105 25

5 252

22

3232

What if the numerator is not 1

Evaluate

42

22

3232

2

5 105 25

5 252

For any nonzero real number b, and integer m and n

Make sure the Radical express is real, no b<0 when n is even.

mnn mnm

borbb

Simplify each expression

No fraction in the denominators.

32

74

71

x

yy

Simplify

31

61

3

6

2

16216

Simplify

31

64

31

61

4

31

61

3

6

2

2

2

)2(

2

16216

Simplify

331

31

32

31

32

31

64

31

61

4

31

61

3

6

22222

2

2

2

2

)2(

2

16216

Simplify

6 44x

Simplify

64

61

6 4 44 xx

Simplify

64

61

2

64

61

6 4

2

44

x

xx

Simplify

64

62

64

61

2

64

61

6 4

2

2

44

x

x

xx

Simplify

32

31

64

62

64

61

2

64

61

6 4

22

2

44

xx

x

xx

Simplify

3 231

2

32

31

64

62

64

61

2

64

61

6 4

22

22

2

44

xx

xx

x

xx