Review of Introductory Mathematics
EXPONENTS
Fractional Exponents
Fractional exponents are defined as follows,
. This permits manipulations with
a
1
m
n
a
numbers with fractional exponents to be treated using the laws expressed earlier for integers. For
example,
8
1
3
3
8
2
since 2×2×2
8
Taking the statement
and cubing both sides,
. But (am)n = a
m x n
so
8
1
3
2
8
1
3
3
23
which agrees with 23 = 8 for the right-hand side of the equality.
8
1
3
3
81
8
A number such as
can be written
or alternately as
since
8
2
3
8
1
3
2
22
4
82
1
3
64
1
3
4
4 x 4 x 4 = 64; that is, 4 is the cube root of 64.
Examples:
a
1
3
a
2
3
a
1
3
2
3
a1
a
b
1
4
b
1
2
b
1
4
1
2
b
1
2
1
b2
d
1
3
9
d
1
3
×9
d3
Rev. 0
Page 65
MA-01
