rational exponents

1. Rational
Exponents
In other words,
exponents that are
ratios or fractions.

2. Definition of Rational Exponents
For any nonzero number b and
any integers m and n with n > 1,
𝑏
𝑚
𝑛 =
𝑛
𝑏 𝑚 = (
𝑛
𝑏) 𝑚

3. NOTE:
There are 3 different ways to
write a rational exponent…
64
2
3 =
3
642 = (
3
64)2
To simplify,you may need to
write it in another form.

4. Rewrite from
exponential to radical:
1. 36
3
2 = ( 36)3
= (6)3
= 216
2.
3
59=5
9
3 = 53
= 125
Rewrite from radical to
exponential:

5. Examples with negative
powers:
3. 64−
1
2 = ( 1
64
)
1
2=
1
64
=
1
8
4. (1
8
)−
1
3= 8
1
3 =
3
8 = 2

6. Example with a variable:
5.
3
𝑥8
𝑥5
=
𝑥
8
3
𝑥
5
2
= 𝑥
8
3
−
5
2=…
𝑥
8
3
∙
2
2
−
5
2
∙
3
3 = 𝑥
16
6
−
15
6 =…
𝑥
1
6 𝑜𝑟 6
𝑥