Solved Examples and Worksheet for Expressions with Rational Exponents
Q1
Evaluate:
3
4
3
1
3
A
.
1
1029
B
. 1
C
. 7
D
.
343
3
Solutions
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Step: 1
3
4
3
1
3
=
(
7
3
)
1
3
Step: 2
=
(
7
)
3
⋅
1
3
[Use the formula (
a
m
)
n
=
a
m
n
.]
Step: 3
= 7
Correct Answer is :
7
Q2
Evaluate:
7
2
9
1
3
A
.
1
2187
B
. 1
C
. 9
D
. 243
Solutions
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Step: 1
7
2
9
1
3
=
(
9
3
)
1
3
Step: 2
=
(
9
)
3
⋅
1
3
[Use the formula (
a
m
)
n
=
a
m
n
.]
Step: 3
= 9
Correct Answer is :
9
Q3
Evaluate:
(
-
2
1
6
)
2
3
A
. - 144
B
.
1
36
C
. 36
D
. - 36
Solutions
Share
Step: 1
(
-
2
1
6
)
2
3
=
(
-
2
1
6
3
)
2
[Use the formula
a
m
n
=
(
a
n
)
m
.]
Step: 2
= (
(
-
6
)
3
⋅
1
3
)
2
= (- 6)
2
= 36
Correct Answer is :
36
Q4
Evaluate:
121
1.5
A
.
363
2
B
. 121
C
. 1331
D
. 11
Solutions
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Step: 1
121
1.5
=
1
2
1
3
2
Step: 2
= (
1
2
1
)
3
[Use the formula
a
m
n
=
(
a
n
)
m
.]
Step: 3
= (11)
3
Step: 4
= 1331
Correct Answer is :
1331
Q5
Simplify:
(
6
2
5
x
-
1
6
y
2
0
)
-
1
4
A
.
x
4
5
y
5
B
. 625
x
4
y
5
C
. 625
x
4
y
- 5
D
.
1
5
x
4
y
5
Solutions
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Step: 1
(
6
2
5
x
-
1
6
y
2
0
)
-
1
4
=
6
2
5
-
1
4
.
x
-
1
6
(
-
1
4
)
.
y
2
0
(
-
1
4
)
[Use: (
a
l
b
m
c
n
)
p
=
a
lp
b
mp
c
np
.]
Step: 2
=
1
6
2
5
1
4
.
x
4
.
y
- 5
[Use:
a
-
n
=
1
a
n
.]
Step: 3
=
1
6
2
5
4
.
x
4
.
1
y
5
[Use:
a
1
n
=
a
n
.]
Step: 4
=
x
4
5
y
5
Correct Answer is :
x
4
5
y
5
Q6
Evaluate:
(25)
1.5
A
. 121.5
B
. 25
C
. 5
D
. 125
Solutions
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Step: 1
(25)
1. 5
=
2
5
3
2
=
(
2
5
)
3
[Use the formula
a
m
n
=
(
a
n
)
m
.]
Step: 2
= 5
3
Step: 3
= 125
Correct Answer is :
125
Q7
Evaluate:
(
-
1
6
3
8
4
)
1
7
A
. -
16384
7
B
. 4
C
. - 4
D
.
16384
7
Solutions
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Step: 1
(
-
1
6
3
8
4
)
1
7
=
(
-
4
7
)
1
7
Step: 2
=
(
-
4
)
7
⋅
1
7
[Use the formula (
a
m
)
n
=
a
m
n
.]
Step: 3
= - 4
Correct Answer is :
- 4
Q8
Evaluate:
(
6
4
⋅
8
4
)
-
5
6
A
.
8
-
5
3
6
B
.
1
8
5
C
.
1
40
D
.
8
5
Solutions
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Step: 1
(
6
4
⋅
8
4
)
-
5
6
=
(
8
2
⋅
8
4
)
-
5
6
Step: 2
=
(
8
2
+
4
)
-
5
6
[Use
a
m
.
a
n
=
a
m
+
n
.]
Step: 3
=
8
6
⋅
(
-
5
6
)
[Use (
a
m
)
n
=
a
mn
.]
Step: 4
= 8
- 5
=
1
8
5
[Use
a
-
n
=
1
a
n
.]
Step: 5
=
1
8
5
Correct Answer is :
1
8
5
Q9
Evaluate:
7
(
-
5
1
2
)
-
1
3
A
.
7
8
B
.
3584
3
C
. 56
D
. -
7
8
Solutions
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Step: 1
7
(
-
5
1
2
)
-
1
3
=
7
(
-
5
1
2
)
1
3
[Use
1
a
n
=
a
-
n
.]
Step: 2
=
7
-
5
1
2
3
[Use
a
1
n
=
a
n
.]
Step: 3
=
7
(-8)
Step: 4
= -
7
8
Correct Answer is :
-
7
8
Q10
Evaluate:
2
7
-
2
3
A
.
1
9
B
. 9
C
.
3
7
9
3
D
. - 18
Solutions
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Step: 1
2
7
-
2
3
=
(
3
3
)
-
2
3
Step: 2
3
3
(
-
2
3
)
[Using (
a
m
)
n
=
a
mn
.]
Step: 3
= 3
- 2
[Use
a
-
n
=
1
a
n
.]
Step: 4
=
1
3
2
Step: 5
=
1
9
Correct Answer is :
1
9
Q11
Simplify:
(
9
y
2
3
)
- 1
A
. -
9
y
3
y
B
.
y
3
9
C
. 9
y
3
2
D
.
y
3
9
y
Solutions
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Step: 1
(
9
y
2
3
)
-1
= 9
- 1
.
y
2
3
(
-
1
)
[Use (
a
m
b
n
)
p
=
a
mp
b
np
.]
Step: 2
= 9
- 1
.
y
-
2
3
Step: 3
=
1
9
.
1
y
2
3
[Use
a
-
n
=
1
a
n
.]
Step: 4
=
1
9
y
2
3
Step: 5
=
y
3
9
y
Correct Answer is :
y
3
9
y
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