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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
( )
( )
( )
( )
( ) ( )
( ) ( )
( )
( )
( )
( )
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FAQs on RS Aggarwal Solutions: Exponents - Mathematics (Maths) Class 7
| 1. What are exponents in mathematics? |  |
Ans. Exponents are a mathematical notation used to represent repeated multiplication of a number by itself. It consists of a base number raised to a power or exponent. For example, in the expression 2^3, 2 is the base number and 3 is the exponent. It means 2 multiplied by itself three times, which is equal to 2 x 2 x 2 = 8.
| 2. How do you read exponents? | |
Ans. Exponents are read in different ways. For example, 2^3 can be read as "2 raised to the power of 3" or "2 to the third power". Similarly, 5^2 can be read as "5 squared" or "5 raised to the power of 2". The notation and reading may vary, but the concept remains the same.
| 3. What are the rules of exponents? | |
Ans. There are several rules of exponents that help simplify and manipulate expressions involving exponents. Some of the common rules include:
- Product Rule: When multiplying two numbers with the same base, add their exponents.
- Quotient Rule: When dividing two numbers with the same base, subtract their exponents.
- Power Rule: When raising a number with an exponent to another exponent, multiply the exponents.
- Zero Rule: Any number (except zero) raised to the power of 0 is equal to 1.
- Negative Exponent Rule: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
| 4. How are exponents used in real-life situations? | |
Ans. Exponents are used in various real-life situations such as finance, science, and engineering. For example, compound interest calculations involve exponential growth or decay. In physics, the concept of exponential decay is used to model radioactive decay. Exponents also play a crucial role in computer science and data analysis, where large or small numbers are represented using scientific notation.
| 5. How can I solve problems involving exponents? | |
Ans. To solve problems involving exponents, it is important to understand the basic rules and properties of exponents. Start by simplifying the expressions using these rules. If necessary, convert numbers to scientific notation for easier calculations. Practice solving different types of problems, such as finding the value of an expression, simplifying expressions, or solving equations with exponents. Regular practice and familiarity with the rules will help improve problem-solving skills in this area.
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RS Aggarwal Solutions: Exponents Class 7 Questions
The "RS Aggarwal Solutions: Exponents Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
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The content of RS Aggarwal Solutions: Exponents is prepared as per the latest Class 7 syllabus.
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