Rational Exponents Worksheet
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3NAME _____________________________________________ DATE ____________________________ PERIOD _____________
6-6 Study Guide and Intervention
Rational Exponents
Rational Exponents and Radicals
1
��
��
For any real number b and any positive integer n, ��
Definition of ��
= √��
, except when b < 0 and n is even.
��
��
��
��
��
��
��
Definition of ��
= ( √��
)
For any nonzero real number b, and any integers m and n, with n > 1, ��
= √��
��
��
,
��
except when b < 0 and n is even.
��
��
Write ����
−��
Example 1:
��
in radical form.
��
: Evaluate (
)
Example 2
.
−������
Notice that 28 > 0.
Notice that –8 < 0, –125 < 0, and 3 is odd.
1
28
= √ 28
1
2
3
−8
√ −8
3
(
)
=
3
2
= √2
⋅ 7
−125
√ −125
−2
=
= √2
2
⋅ √ 7
−5
2
= 2 √ 7
=
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
3
4
5
2
5
4. √ 47
5. √3��
��
6. √162��
Evaluate each expression.
2
1
1
7. −27
8. 216
9. (0.0004)
3
3
2
38
Chapter 6
Glencoe Algebra 2
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