Rational Exponents
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1
2NAME
DATE
PERIOD
6-6
Study Guide and Intervention
Rational Exponents
Rational Exponents and Radicals
For any real number b and any positive integer n,
1
−
Definition of b
n
1
n
−
√ b , except when b < 0 and n is even.
b
=
n
For any nonzero real number b, and any integers m and n, with n > 1,
m
−
Definition of b
m
n
(
)
m
n
−
n
√ b
√
m
b
=
=
b
, except when b < 0 and n is even.
n
1
(
)
1
-8
Example 1
Example 2
−
−
Write 28
in radical form.
Evaluate
−
.
3
2
-125
Notice that 28 > 0.
Notice that -8 < 0, -125 < 0, and 3 is odd.
1
−
= √ 28
28
3
2
1
√ -8
(
)
-8
−
−
=
−
3
= √ 2
-125
3
2
7
√ -125
-2
= √ 2
√ 7
2
−
=
-5
= 2 √ 7
2
=
−
5
Exercises
Write each expression in radical form, or write each radical in exponential form.
1
1
3
−
−
−
1. 11
2. 15
3. 300
7
3
2
7
3
√ 11
√ 15
3000 √ 3
3
4
√ 3a
√
4. √ 47
5.
5
b
2
6.
162p
5
1
1
5
2
1
5
−
−
−
−
−
−
47
3
a
b
3 2
p
2
3
3
3
4
4
Evaluate each expression.
2
1
1
−
−
−
7. -27
8. 216
9. (0.0004)
2
3
3
9
6
0.02
38
Chapter 6
Glencoe Algebra 2
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