Exponents And Radicals Worksheets Page 14
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15Rational Exponents
Definition:
If a is a real number and n is a positive integer
1
=
n
n
a
a
such that the principal nth root of a exists, then
where
1/n is the rational exponent of a. Moreover, if m is a positive
integer that has no common factor with n, then
m
1
1
=
=
=
=
m
m
m
n
m
n
n
n
n
a
(
a
)
(
a
)
(
a
)
a
.
Examples:
Evaluate or simplify:
1
9
−
( )
2
4
4
1
−
−
3
(
)
125
12
5
8
2
5
8
1
5
−
⋅
2
2
5
5
x
3
(5 )
x
2
M161c1s2p2
14
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