Write Each Expression In Radical Form
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1
2
3Lesson 5–7
Example 1
Radical Form
Write each expression in radical form.
1
1
a.
36
3
b.
9
z
1
1
1
1
3
9
b
9
b
36
3
=
36
Definition of
n
z
=
z
Definition of
n
Example 2
Exponential Form
Write each radical using rational exponents.
7
5
a.
b.
29
a
1
1
1
1
7
5
b
b
a
= a
7
Definition of
n
= 29
5
Definition of
n
29
Example 3
Evaluate Expressions with Rational Exponents
Evaluate each expression.
1
–
6
a. 729
Method 1
Method 2
1
1
1
( )
1
1
–
–
–
6
–n
6
6
6
729
=
b
=
729
= 3
729 = 3
6
1
n
b
6
729
1
1
1
6 –
6
6
6
=
729
=
729
= 3
Power of a Power
6
729
1
–1
= 3
Multiply exponents.
6
=
729 = 3
6
6
3
1
1
1
–1
=
Simplify.
=
3
=
1
3
3
3
2
b. 343
3
Method 1
Method 2
1
2
2
2
( )
2
3
3
3
343
3
= 7
343 = 7
3
3
343
= 343
Factor.
1
2
(
)
3
2
= 343
Power of a Power
3
3
= 7
Power of a Power
2
1
= 7
Multiply exponents.
3
2
=
3
3
=
343
b
b
2
= 49
7
= 49
3
2
3
3
(
)
=
7
343 = 7
3
3
3
•
=
7
7
Expand the square.
= 7 • 7 or 49
Find the cube root.
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