Rational Exponents
The Rule for Rational Exponents
1
n
b  b
n
1
3
64  64  4
3
How would we simplify this
expression?
What does the fraction exponent do to the
number?
9
1
2
The number can be written as a Radical
expression, with an index of the
denominator. 2
9
Write in Radical form
1
6
a 
1
2
m 
Write in Radical form
1
6
a  a
1
2
6
m  m
Write each Radical using Rational
Exponents
5
b
w
Write each Radical using Rational
Exponents
5
b b
1
5
ww
1
2
What about Negative exponents
Negative exponents make inverses.
49
1
2

1
49
1
2
1

7
What if the numerator is not 1
Evaluate
2
5
32  32
5
2
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.
m
n
b  b or
n
m
 b
n
m
What if the numerator is not 1
Evaluate
2
5
32  32
5
5
2 
5 2
2
 2
5
10
What if the numerator is not 1
Evaluate
2
5
32  32
5
5
2 
5 2
2 4
2
2
 2
5
10
Simplify each expression
1
7
y y
x
2
3
4
7
Simplify
6
1
6
16 16
 1
3
2
23
Simplify
1
6
6
16 16
 1
3
2
23

1
4 6
(2 )
2
1
3

2
2
4
6
1
3
Simplify
1
6
6
16 16
 1
3
2
23

1
4 6
(2 )
2

2
2
2
3
1
3
1
3

2
2
2
3
4
6
1
3
1
3
1
3
2 2 2 3 2
Simplify
6
4x
4
Simplify
6
1
6
4x4  4 x
4
6
Simplify
6
1
6
4x  4 x
4
 x
 2
1
2 6
4
6
4
6
Simplify
6
1
6
4x4  4 x
 x
 2
1
2 6
2
6
2 x
4
6
4
6
4
6
Simplify
6
1
6
4x4  4 x
 2

1
2 6
2
6
4
6
x
4
6
4
6
1
3
2 x 2 x
2
3
Simplify
6
1
6
4x  4 x
4
 
 2
1
2 6
2
6
x
4
6
4
6
4
6
1
3
2 x 2 x
 
 2x
1
2 3
2
3
 3 2x2
Practice Problems