Radical Expressions And Rational Exponents Worksheet Page 3
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1
2
3
43
E X A M P L E
Writing Expressions in Radical Form
_
2
(
)
-125
Write the expression
in radical form, and simplify.
3
Method 1 Evaluate the root first.
Method 2 Evaluate the power first.
(
)
√
2
(
)
3
√ -125
3
2
-125
Write with a radical.
Write with a radical.
The denominator of
(
)
√
-5
2
3
15,625
Evaluate the root.
Evaluate the power.
a rational exponent
becomes the index of
25
25
Evaluate the power.
Evaluate the root.
the radical.
Write each expression in radical form, and simplify.
1 _
5 _
3 _
3
2
4
3a. 64
3b. 4
3c. 625
4
E X A M P L E
Writing Expressions by Using Rational Exponents
Write each expression by using rational exponents.
√
√
4
3
3
6
A
B
7
11
3 _
6 _
m _
m _
√ a
√ a
n
= a
n
= a
4
m
3
m
7
n
11
n
2
11
= 121
Simplify.
Write each expression by using rational exponents.
(
)
3
√
√
3
4
√ 81
4
9
2
4a.
4b.
10
4c.
5
Rational exponents have the same properties as integer exponents.
(See Lesson 1-5.)
Properties of Rational Exponents
For all nonzero real numbers a and b and rational numbers m and n,
WORDS
NUMBERS
ALGEBRA
Product of Powers Property
1 _
3 _
1 _
+ 3 _
· a
=
To multiply powers with the
m
n
a
· 12
= 12
= 12
= 144
2
2
2
2
2
12
m + n
same base, add the exponents.
a
Quotient of Powers Property
2 _
To divide powers with the
2 _
- 1 _
1 _
m
3
125
a
_
_
m - n
= 125
= 125
= 5
= a
same base, subtract the
3
3
3
n
1 _
a
exponents.
3
125
Power of a Power Property
(
)
3
2 _
To raise one power to another,
2 _
· 3
(
)
n
m · n
= 8
= 8
= 64
= a
2
m
3
8
a
3
multiply the exponents.
Power of a Product Property
1 _
1 _
To find the power of a
1 _
(
)
16 · 25
= 16
· 25
= 4 · 5
2
2
2
(
)
m
= a
m
m
product, distribute the
ab
b
= 20
exponent.
Power of a Quotient Property
1 _
To find the power of a
(
)
1 _
(
)
4
16
= 16
= 2 _
m
m
_
_
a _
= a
_
4
quotient, distribute the
81
1 _
3
m
b
b
exponent.
4
81
612
612
Chapter 8 Rational and Radical Functions
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