Rational Exponents Worksheet Page 2
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3NAME _____________________________________________ DATE ____________________________ PERIOD _____________
6-6 Study Guide and Intervention
(continued)
Rational Exponents
Simplify Expressions
All the properties of powers from Lesson 6-1 apply to rational exponents. When you simplify
expressions with rational exponents, leave the exponent in rational form, and write the expression with all positive
exponents. Any exponents in the denominator must be positive integers.
When you simplify radical expressions, you may use rational exponents to simplify, but your answer should be in radical
form. Use the smallest index possible.
��
��
⋅
: Simplify ��
��
Example 1
��
.
��
��
��
Simplify √��������
Example 2:
.
2
3
2
3
25
+
1
⋅
��
��
= ��
= ��
4
6
3
8
3
8
24
= ( 144��
)
√144��
6
4
1
4
2
6
= ( 2
)
⋅ 3
⋅ ��
4
1
1
1
4
2
6
= ( 2
)
⋅
( 3
)
⋅
( ��
)
4
4
4
1
3
1
( 3�� )
⋅
⋅
= 2 ⋅ 3
��
= 2x √ 3��
2
2
= 2x
2
Exercises
Simplify each expression.
3
4
6
2
4
7
4
1. ��
⋅ ��
2. (��
)
3. ��
⋅ ��
5
5
3
5
10
2
4
6
3
4
1
5
3
4. (��
)
⋅
6. (��
)
5. ��
��
5
8
3
6
1
��
��
2
6
9. √ 128
7.
8.
1
1
��
3
��
3
4
5
10. √ 49
11. √ 288
12. √ 32 ⋅ 3 √ 16
3
4
�� √��
3
6
13. √25
⋅ √125
14. √ 16
15.
3
√����
39
Chapter 6
Glencoe Algebra 2
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