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Page 1
Question:1
Write each of the following in power notation:
i
5
7
×
5
7
×
5
7
×
5
7
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
iii
-1
6
×
-1
6
×
-1
6
iv
-8
× -8
× -8
× -8
× -8
Solution:
i
5
7
×
5
7
×
5
7
×
5
7
=
5
7
4
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
=
-4
3
5
iii
-1
6
×
-1
6
×
-1
6
=
-1
6
3
iv
(-8)×(-8)×(-8)×(-8)×(-8) = (-8)
5
Question:2
Express each of the following in power notation:
i
25
36
ii
-27
64
iii
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
Page 2
Question:1
Write each of the following in power notation:
i
5
7
×
5
7
×
5
7
×
5
7
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
iii
-1
6
×
-1
6
×
-1
6
iv
-8
× -8
× -8
× -8
× -8
Solution:
i
5
7
×
5
7
×
5
7
×
5
7
=
5
7
4
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
=
-4
3
5
iii
-1
6
×
-1
6
×
-1
6
=
-1
6
3
iv
(-8)×(-8)×(-8)×(-8)×(-8) = (-8)
5
Question:2
Express each of the following in power notation:
i
25
36
ii
-27
64
iii
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
-32
243
iv
-1
128
Solution:
i
25
36
=
5
2
6
2
[since 25 = 5
2
and 36 = 6
2
]
=
5
6
2
ii
-27
64
=
(-3)
3
4
3
[since -27 = (-3)
3
and 64 = 4
3
]
=
-3
4
3
iii
-32
243
=
(-2)
5
3
5
[since -32 = (-2)
5
and 243 = 3
5
]
=
-2
3
5
iv
-1
128
=
(-1)
7
2
7
[since (-1)
7
= -1 and 128 = 2
7
]
=
-1
2
7
Question:3
Express each of the following as a rational number:
i
2
3
5
ii
-8
5
3
iii
-13
11
2
iv
( )
( )
( )
( )
( )
( )
( )
( )
Page 3
Question:1
Write each of the following in power notation:
i
5
7
×
5
7
×
5
7
×
5
7
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
iii
-1
6
×
-1
6
×
-1
6
iv
-8
× -8
× -8
× -8
× -8
Solution:
i
5
7
×
5
7
×
5
7
×
5
7
=
5
7
4
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
=
-4
3
5
iii
-1
6
×
-1
6
×
-1
6
=
-1
6
3
iv
(-8)×(-8)×(-8)×(-8)×(-8) = (-8)
5
Question:2
Express each of the following in power notation:
i
25
36
ii
-27
64
iii
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
-32
243
iv
-1
128
Solution:
i
25
36
=
5
2
6
2
[since 25 = 5
2
and 36 = 6
2
]
=
5
6
2
ii
-27
64
=
(-3)
3
4
3
[since -27 = (-3)
3
and 64 = 4
3
]
=
-3
4
3
iii
-32
243
=
(-2)
5
3
5
[since -32 = (-2)
5
and 243 = 3
5
]
=
-2
3
5
iv
-1
128
=
(-1)
7
2
7
[since (-1)
7
= -1 and 128 = 2
7
]
=
-1
2
7
Question:3
Express each of the following as a rational number:
i
2
3
5
ii
-8
5
3
iii
-13
11
2
iv
( )
( )
( )
( )
( )
( )
( )
( )
1
6
3
v
-1
2
5
vi
-3
2
4
vii
-4
7
3
viii
-1
9
Solution:
i
2
3
5
=
(2)
5
(3)
5
=
2×2×2×2×2
3×3×3×3×3
=
32
243
ii
-8
5
3
=
(-8)
3
(5)
3
=
(-8)×(-8)×(-8)
5×5×5
=
-512
125
iii
-13
11
2
=
(-13)
2
(11)
2
=
(-13)×(-13)
11×11
=
169
121
iv
1
6
3
=
(1)
3
(6)
3
=
1×1×1
6×6×6
=
1
216
v
-1
2
5
=
(-1)
5
(2)
5
=
(-1)×(-1)×(-1)×(-1)×(-1)
2×2×2×2×2
=
-1
32
vi
-3
2
4
=
(-3)
4
(2)
4
=
(-3)×(-3)×(-3)×(-3)
2×2×2×2
=
81
16
vii
-4
7
3
=
(-4)
3
(7)
3
=
(-4)×(-4)×(-4)
7×7×7
=
-64
343
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
Page 4
Question:1
Write each of the following in power notation:
i
5
7
×
5
7
×
5
7
×
5
7
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
iii
-1
6
×
-1
6
×
-1
6
iv
-8
× -8
× -8
× -8
× -8
Solution:
i
5
7
×
5
7
×
5
7
×
5
7
=
5
7
4
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
=
-4
3
5
iii
-1
6
×
-1
6
×
-1
6
=
-1
6
3
iv
(-8)×(-8)×(-8)×(-8)×(-8) = (-8)
5
Question:2
Express each of the following in power notation:
i
25
36
ii
-27
64
iii
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
-32
243
iv
-1
128
Solution:
i
25
36
=
5
2
6
2
[since 25 = 5
2
and 36 = 6
2
]
=
5
6
2
ii
-27
64
=
(-3)
3
4
3
[since -27 = (-3)
3
and 64 = 4
3
]
=
-3
4
3
iii
-32
243
=
(-2)
5
3
5
[since -32 = (-2)
5
and 243 = 3
5
]
=
-2
3
5
iv
-1
128
=
(-1)
7
2
7
[since (-1)
7
= -1 and 128 = 2
7
]
=
-1
2
7
Question:3
Express each of the following as a rational number:
i
2
3
5
ii
-8
5
3
iii
-13
11
2
iv
( )
( )
( )
( )
( )
( )
( )
( )
1
6
3
v
-1
2
5
vi
-3
2
4
vii
-4
7
3
viii
-1
9
Solution:
i
2
3
5
=
(2)
5
(3)
5
=
2×2×2×2×2
3×3×3×3×3
=
32
243
ii
-8
5
3
=
(-8)
3
(5)
3
=
(-8)×(-8)×(-8)
5×5×5
=
-512
125
iii
-13
11
2
=
(-13)
2
(11)
2
=
(-13)×(-13)
11×11
=
169
121
iv
1
6
3
=
(1)
3
(6)
3
=
1×1×1
6×6×6
=
1
216
v
-1
2
5
=
(-1)
5
(2)
5
=
(-1)×(-1)×(-1)×(-1)×(-1)
2×2×2×2×2
=
-1
32
vi
-3
2
4
=
(-3)
4
(2)
4
=
(-3)×(-3)×(-3)×(-3)
2×2×2×2
=
81
16
vii
-4
7
3
=
(-4)
3
(7)
3
=
(-4)×(-4)×(-4)
7×7×7
=
-64
343
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
viii
(-1)
9
= -1
[Since (-1)
an odd natural number
= -1]
Question:4
Express each of the following as a rational number:
i
4
-1
ii
-6
-1
iii
1
3
-1
iv
-2
3
-1
Solution:
i
(4)
-1
=
4
1
-1
=
1
4
1
=
1
4
[since
a
b
-n
=
b
a
n
]
ii
(-6)
-1
=
-6
1
-1
=
1
-6
1
=
-1
6
[since
a
b
-n
=
b
a
n
]
iii
1
3
-1
=
3
1
1
=
3
1
[since
a
b
-n
=
b
a
n
]
iv
-2
3
-1
=
3
-2
1
=
-3
2
[since
a
b
-n
=
b
a
n
]
( )
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Page 5
Question:1
Write each of the following in power notation:
i
5
7
×
5
7
×
5
7
×
5
7
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
iii
-1
6
×
-1
6
×
-1
6
iv
-8
× -8
× -8
× -8
× -8
Solution:
i
5
7
×
5
7
×
5
7
×
5
7
=
5
7
4
ii
-4
3
×
-4
3
×
-4
3
×
-4
3
×
-4
3
=
-4
3
5
iii
-1
6
×
-1
6
×
-1
6
=
-1
6
3
iv
(-8)×(-8)×(-8)×(-8)×(-8) = (-8)
5
Question:2
Express each of the following in power notation:
i
25
36
ii
-27
64
iii
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
-32
243
iv
-1
128
Solution:
i
25
36
=
5
2
6
2
[since 25 = 5
2
and 36 = 6
2
]
=
5
6
2
ii
-27
64
=
(-3)
3
4
3
[since -27 = (-3)
3
and 64 = 4
3
]
=
-3
4
3
iii
-32
243
=
(-2)
5
3
5
[since -32 = (-2)
5
and 243 = 3
5
]
=
-2
3
5
iv
-1
128
=
(-1)
7
2
7
[since (-1)
7
= -1 and 128 = 2
7
]
=
-1
2
7
Question:3
Express each of the following as a rational number:
i
2
3
5
ii
-8
5
3
iii
-13
11
2
iv
( )
( )
( )
( )
( )
( )
( )
( )
1
6
3
v
-1
2
5
vi
-3
2
4
vii
-4
7
3
viii
-1
9
Solution:
i
2
3
5
=
(2)
5
(3)
5
=
2×2×2×2×2
3×3×3×3×3
=
32
243
ii
-8
5
3
=
(-8)
3
(5)
3
=
(-8)×(-8)×(-8)
5×5×5
=
-512
125
iii
-13
11
2
=
(-13)
2
(11)
2
=
(-13)×(-13)
11×11
=
169
121
iv
1
6
3
=
(1)
3
(6)
3
=
1×1×1
6×6×6
=
1
216
v
-1
2
5
=
(-1)
5
(2)
5
=
(-1)×(-1)×(-1)×(-1)×(-1)
2×2×2×2×2
=
-1
32
vi
-3
2
4
=
(-3)
4
(2)
4
=
(-3)×(-3)×(-3)×(-3)
2×2×2×2
=
81
16
vii
-4
7
3
=
(-4)
3
(7)
3
=
(-4)×(-4)×(-4)
7×7×7
=
-64
343
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
viii
(-1)
9
= -1
[Since (-1)
an odd natural number
= -1]
Question:4
Express each of the following as a rational number:
i
4
-1
ii
-6
-1
iii
1
3
-1
iv
-2
3
-1
Solution:
i
(4)
-1
=
4
1
-1
=
1
4
1
=
1
4
[since
a
b
-n
=
b
a
n
]
ii
(-6)
-1
=
-6
1
-1
=
1
-6
1
=
-1
6
[since
a
b
-n
=
b
a
n
]
iii
1
3
-1
=
3
1
1
=
3
1
[since
a
b
-n
=
b
a
n
]
iv
-2
3
-1
=
3
-2
1
=
-3
2
[since
a
b
-n
=
b
a
n
]
( )
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Question:5
Find the reciprocal of each of the following:
i
3
8
4
ii
-5
6
11
iii
6
7
iv
-4
3
Solution:
We know that the reciprocal of
a
b
m
is
b
a
m
.
i
Reciprocal of
3
8
4
=
8
3
4
ii
Reciprocal of
-5
6
11
=
-6
5
11
iii
Reciprocal of 6
7
= Reciprocal of
6
1
7
=
1
6
7
iv
Reciprocal of -4
3
= Reciprocal of
-4
1
3
=
-1
4
3
Question:6
Find the value of each of the following:
i
( )
( )
( )
( )
( ) ( )
( ) ( )
( )
( )
( )
( )
Read MoreFAQs on RS Aggarwal Solutions: Exponents
| 1. What's the difference between base and exponent in Class 7 maths? |  |
Ans. The base is the number being multiplied repeatedly, while the exponent (or power) tells how many times to multiply it. For example, in 2⁵, 2 is the base and 5 is the exponent, meaning 2 × 2 × 2 × 2 × 2. Understanding this distinction helps solve exponential expressions correctly and forms the foundation for working with powers in CBSE Class 7 mathematics.
| 2. How do I simplify expressions with negative exponents? | |
Ans. Negative exponents indicate reciprocals. For example, 2⁻³ equals 1/2³ or 1/8. To simplify, convert the negative power to its positive reciprocal form, then calculate. This rule applies universally across exponential notation problems. Practise with flashcards and MCQ tests available on EduRev to master negative exponent rules quickly before your exams.
| 3. Why do I get confused between laws of exponents and regular multiplication? | |
Ans. Laws of exponents apply only when bases are identical-you add exponents when multiplying same bases (aᵐ × aⁿ = aᵐ⁺ⁿ) but cannot simplify unlike bases this way. Regular multiplication handles different numbers directly. This conceptual confusion disappears once you recognise that exponential rules are shortcuts for repeated multiplication of identical factors, not general arithmetic operations.
| 4. What happens when the exponent is zero in CBSE Class 7 exponents? | |
Ans. Any non-zero number raised to the power of zero equals 1. So 5⁰ = 1, 100⁰ = 1, and x⁰ = 1 (where x ≠ 0). This might seem strange initially, but it follows logically from the law of division of powers. Refer to mind maps and detailed notes on EduRev to visualise why this rule holds true consistently.
| 5. How do I compare which is bigger: 2⁵ or 5²? | |
Ans. Calculate each separately: 2⁵ = 32 and 5² = 25, so 2⁵ is larger. Don't assume larger exponents always mean larger results-the base matters significantly. When comparing exponential expressions, compute the actual values rather than guessing from exponent size alone. This comparison skill is essential for solving word problems and ranking numbers in ascending or descending order.
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May 12, 2026 Last updated
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