Solved Examples and Worksheet for Converting Radical and Rational Exponent Form
Q1
What is the radical form of
x
1
7
?
A
.
1
x
7
B
.
x
7
C
.
x
7
D
.
7
x
7
Solutions
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Step: 1
x
1
7
=
x
7
[Use the formula
a
1
n
=
a
n
.]
Correct Answer is :
x
7
Q2
What is the radical form of
x
9
1
0
?
A
.
x
9
1
0
B
.
x
1
0
9
C
.
x
1
1
0
9
D
.
1
1
0
x
9
Solutions
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Step: 1
x
9
1
0
=
(
x
9
)
1
1
0
Step: 2
=
x
9
1
0
or
(
x
1
0
)
9
[Use the formula
a
m
n
=
a
m
n
or
(
a
n
)
m
.]
Correct Answer is :
x
9
1
0
Q3
Express
(
a
7
)
6
in exponential form.
A
.
a
7
6
B
.
a
7
C
.
a
6
7
D
.
a
42
Solutions
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Step: 1
(
a
7
)
6
=
(
a
1
7
)
6
=
a
6
7
[Use the formula
a
m
n
=
a
m
n
.]
Correct Answer is :
a
6
7
Q4
Express
3
x
9
in exponential form.
A
.
3
x
9
B
. (3
x
)
9
C
.
(
3
x
)
1
9
D
. 3 ·
x
1
9
Solutions
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Step: 1
3
x
9
=
(
3
x
)
1
9
[Use the formula
a
b
n
=
(
a
b
)
1
n
.]
Correct Answer is :
(
3
x
)
1
9
Q5
Express
3
⋅
x
-
7
8
in exponential form.
A
.
3
1
8
⋅
x
1
8
x
B
.
3
1
8
⋅
x
1
8
x
2
C
.
3
1
8
⋅
x
1
8
x
4
D
.
3
8
⋅
x
1
8
x
Solutions
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Step: 1
3
⋅
x
-
7
8
=
(
3
⋅
x
-
7
)
1
8
[Use the formula
a
b
n
=
(
a
b
)
1
n
.]
Step: 2
=
3
1
8
⋅
x
-
7
8
Step: 3
=
3
1
8
⋅
x
1
8
x
Correct Answer is :
3
1
8
⋅
x
1
8
x
Q6
Express
7
x
8
in exponential form.
A
.
(
7
x
)
1
8
B
. 7
x
8
C
.
7
x
1
8
D
.
x
7
8
Solutions
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Step: 1
7
x
8
=
7
x
1
8
[Use the formula
a
n
=
a
1
n
.]
Correct Answer is :
7
x
1
8
Q7
What is the radical form of the expression (16384)
1
6
?
A
. 4
4
6
B
. 16384
C
.
4
6
D
. 3
4
6
Solutions
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Step: 1
(16384)
1
6
=
1
6
3
8
4
6
[Use
a
1
n
=
a
n
.]
Step: 2
=
(
4
6
×
4
)
6
Step: 3
= 4
4
6
[Simplify.]
Correct Answer is :
4
4
6
Q8
Find the radical form of (10)
1
8
?
A
.
1
0
5
B
.
4
8
C
.
5
8
D
.
1
0
8
Solutions
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Step: 1
The radical form of (a)
1
n
is
a
n
.
[Formula.]
Step: 2
The radical form of (10)
1
8
is
1
0
8
.
Correct Answer is :
1
0
8
Q9
Identify the radical form of the expression (625)
2
3
?
A
. 5(
5
3
)
2
B
. 4(
5
3
)
2
C
. 25(
5
3
)
2
D
. 16(
5
3
)
2
Solutions
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Step: 1
(625)
2
3
= (
6
2
5
3
)
2
[Use
a
1
n
=
a
n
.]
Step: 2
= (
5
3
×
5
3
)
2
[625 = 5 × 5 × 5 × 5 =
5
3
× 5.]
Step: 3
(5
5
3
)
2
[Simplify.]
Step: 4
= 25(
5
3
)
2
[(
ab
)
2
=
a
2
b
2
.]
Correct Answer is :
25(
5
3
)
2
Q10
What if the radical form of the expression (729)
1
5
A
.
3
B
. 3
3
5
C
. 3
D
. 3
2
5
Solutions
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Step: 1
(729)
1
5
=
7
2
9
5
[Use
a
1
n
=
a
n
.]
Step: 2
=
(
3
5
×
3
)
5
Step: 3
= 3
3
5
[Simplify.]
Correct Answer is :
3
3
5
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Related Topic
Radicand
Rational Exponents
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