7.3
Rational Exponents
We know that:
Squaring a number and taking the square root are
inverse operations for nonnegative numbers.
There are inverse operations for other powers also:
Operation
Inverse
Cubing
a number
cube 3
(
root
Raising to
the 4th
power
fourth
root (
Example
)
4
3
2 = 8 so
)
4
3
8 = 2
4
3 = 81 so 81 = 3
This is the index of the radical
3
Simplify:
3
5
27
32
144
With your calculator, find:
1
49 2
256
100
1
2
A number raised to the power of
the nth root of that number
Write each expression in radical form:
3
1
2
xy
1
2
1
2
1
54
1
5w 3
1
n
=
You can also have fractional exponents
with a numerator other than 1
Example:
2
83
= 8
1
3
2
1
3
2
( (
= 8
=
( 8(
2
3
2
=
(2 (
=
4
Simplify:
25
3
2
4
643
1
2
((
81
169
3
2
((
9
16
-3
2
25
1
2
(w (
2
3