NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers
NCERT solutions for class 7 maths chapter 13 Exponents and Powers: If someone asks you about the speed of bus or car, you may say its 40 km/hr but if you have asked about the speed of light in a vacuum, you will say its approximately 300,000,000 m/s. This is a very big number which is very difficult to write, interpret, and handle. To make any number to represent in an easy way there is a system called exponents. In this article, you will get CBSE NCERT solutions for class 7 maths chapter 13 exponents and powers. Exponents can be used to represent very large numbers and small numbers as the power of a base number. In the above example, you can write 300,000,000 m/s as . Important topics like laws of exponents, multiplying and dividing the power with the same base, multiplying and dividing the powers with the same exponents and expressing large numbers in the standard form are covered in this chapter. There are many questions from the above topics in the solutions of NCERT for class 7 maths chapter 13 exponents and powers that are explained in a stepbystep manner. It will be very easy for you to understand the concepts. In this chapter, there are 17 questions in the 3 exercises of the NCERT textbook. You will get detailed explanations of all these questions in the CBSE NCERT solutions for class 7 maths chapter 13 exponents and powers. Check NCERT solutions from class 6 to 12 by clicking on the above link. Here you will get solutions to three exercises of this chapter.
The main topics of NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers are:
13.1 Introduction
13.2 Exponents
13.3 Laws Of Exponents
13.3.1 Multiplying Powers With The Same Base
13.3.2 Dividing Powers With The Same Base
13.3.3 Taking Power Of A Power
13.3.4 Multiplying Powers With The Same Exponents
13.3.5 Dividing Powers With The Same Exponents
13.4 Miscellaneous Examples Using The Laws Of Exponents
13.5 Decimal Number System
13.6 Expressing Large Numbers In The Standard Form
The NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers are given below:
Solutions of NCERT for class 7 maths chapter 13 exponents and powers topic 13.2 exponents
Question:(i) Express:
Answer:
729 as a power of 3 is given as
CBSE NCERT solutions for class 7 maths chapter 13 exponents and powersExercise: 13.1
Question: 1(i) Find the value of:
Answer:
the value of is given by
Question: 1(iv) Find the value of:
Answer:
the value of is given by
Question: 2 Express the following in exponential form:
Answer:
can be given as
.
can be given as .
can be given as .
can be given as
.
can be given as
.
can be given as
.
Question: 3 Express each of the following numbers using exponential notation:
(i) 512 (ii) 343 (iii) 729 (iv) 3125
Answer:
(i) 512
2 
512 
2 
256 
2 
128 
2 
64 
2 
32 
2 
16 
2 
8 
2 
4 
2 
2 

1 
(ii) 343
7 
343 
7 
49 
7 
7 

1 
(iii)729
3 
729 
3 
243 
3 
81 
3 
27 
3 
9 
3 
3 

1 
(iv)3125
5 
3125 
5 
625 
5 
125 
5 
25 
5 
5 

1 
Question: 4 Identify the greater number, wherever possible, in each of the following?
Answer:
since
is greater than
since
is greater than
since
is greater than
since
is greater than
since
is greater than
Question: 5 Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405 (iii) 540 (iv) 3,600
Answer:
(i) 648
2 
648 
2 
324 
2 
162 
2 
81 
3 
27 
3 
9 
3 
3 

1 
(ii) 405
5 
405 
3 
81 
3 
27 
3 
9 
3 
3 

1 
(iii)540
2 
540 
2 
270 
3 
135 
3 
45 
3 
15 
5 
5 

1 
(iv) 3600
2 
3600 
2 
1800 
2 
900 
2 
450 
3 
225 
3 
75 
5 
25 
5 
5 

1 
Question: 6(i) Simplify:
Question: 8 Compare the following numbers:
Answer:
on comparing exponents of base 10.
on comparing exponents of base 10.
Solutions for NCERT class 7 maths chapter 13 exponents and powers topic 13.3.1 multiplying powers with the same base
Question:(i) Simplify and write in exponential form:
Answer:
can be simplified as
Solutions of NCERT for class 7 maths chapter 13 exponents and powers topic 13.3.2 dividing powers with the same base
Question: 1 Simplify and write in exponential form: (eg., )
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Solutions for NCERT class 7 maths chapter 13 exponents and powers topic 13.3.3 taking powers of a powers
Question: Simplify and write the answer in exponential form:
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Solutions of NCERT for class 7 maths chapter 13 exponents and powers topic 13.3.4 multiplying powers with the same exponents
Question: Put into another form using :
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Solutions of NCERT for class 7 maths chapter 13 exponents and powers topic 13.3.5 dividing powers with the same exponents
Question: Put into another form using :
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
CBSE NCERT solutions for class 7 maths chapter 13 exponents and powersExercise: 13.2
Question: 1 Using laws of exponents, simplify and write the answer in exponential form:
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question:2(i) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(ii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(iii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(iv) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(v) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(vi) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(vii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(viii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(ix) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(x) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(xi) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question:2(xii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 3 Say true or false and justify your answer:
Answer:
can be simplified as
Since ,
Thus, it is false
can be simplified as
Since,
Thus, it is false
can be simplified as
Since ,
Thus, it is false
can be simplified as
Since, LHS = RHS
Thus, it is true.
Question: 4 Express each of the following as a product of prime factors only in exponential form:
Answer:
2 
108 
2 
54 
3 
27 
3 
9 
3 
3 

1 
2 
192 
2 
96 
2 
48 
2 
24 
2 
12 
2 
6 
3 
3 

1 
2 
270 
3 
135 
3 
45 
3 
15 
5 
5 

1 
3 
729 
3 
243 
3 
81 
3 
27 
3 
9 
3 
3 

1 
2 
64 
2 
32 
2 
16 
2 
8 
2 
4 
2 
2 

1 
2 
768 
2 
384 
2 
192 
2 
96 
2 
48 
2 
24 
2 
12 
2 
6 
3 
3 

1 
NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.6 expressing large numbers in the standard form
Question: Expand by expressing powers of 10 in the exponential form:
(i) 172 (ii) 5,643 (iii) 56,439 (iv) 1,76,428
Answer:
(i) 172
(ii) 5,643
(iii) 56,439
(iv) 1,76,428
Solutions of NCERT for class 7 maths chapter 13 exponents and powersExercise: 13.3
Question: 1 Write the following numbers in the expanded forms:
279404, 3006194, 2806196, 120719, 20068
Answer:
(i) 279404
(ii) 3006194
(iii) 2806196
(IV) 120719
(V) 20068
Question: 2 Find the number from each of the following expanded forms:
Answer:
Thus, the above problems are simplified in simpler forms.
Question: 3 Express the following numbers in standard form:
(i) 5,00,00,000 (ii) 70,00,000 (iii ) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78
Answer:
(i) 5,00,00,000
(ii) 70,00,000
(iii ) 3,18,65,00,000
(iv) 3,90,878
(v) 39087.8
(vi) 3908.78
Question: 4 Express the number appearing in the following statements in standard form.
(a) The distance between Earth and Moon is 384,000,000 m.
(b) Speed of light in vacuum is 300,000,000 m/s.
(c) Diameter of the Earth is 1,27,56,000 m.
(d) Diameter of the Sun is 1,400,000,000 m.
(e) In a galaxy there are on an average 100,000,000,000 stars.
(f) The universe is estimated to be about 12,000,000,000 years old.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
(i) The earth has 1,353,000,000 cubic km of sea water.
(j) The population of India was about 1,027,000,000 in March, 2001.
Answer:
(a) The distance between Earth and Moon = 384,000,000 m
(b) Speed of light in vacuum =300,000,000 m/s.
(c) Diameter of the Earth = 1,27,56,000 m.
(d) Diameter of the Sun = 1,400,000,000 m.
(e) In a galaxy there are on an average = 100,000,000,000 stars.
(f) The universe is estimated to be about= 12,000,000,000 years old.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated = 300,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
60,230,000,000,000,000,000,000
(i) The earth has 1,353,000,000 cubic km of seawater.
(j) The population of India was about 1,027,000,000 in March 2001.
NCERT Solutions for Class 7 Maths Chapterwise
Chapter No. 
Chapter Name 
Chapter 1 

Chapter 2 
CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals 
Chapter 3 

Chapter 4 
Solutions of NCERT for class 7 maths chapter 4 Simple Equations 
Chapter 5 
CBSE NCERT solutions for class 7 maths chapter 5 Lines and Angles 
Chapter 6 
NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties 
Chapter 7 
Solutions of NCERT for class 7 maths chapter 7 Congruence of Triangles 
Chapter 8  NCERT solutions for class 7 maths chapter 8 comparing quantities 
Chapter 9 
CBSE NCERT solutions for class 7 maths chapter 9 Rational Numbers 
Chapter 10 
NCERT solutions for class 7 maths chapter 10 Practical Geometry 
Chapter 11 
Solutions of NCERT for class 7 maths chapter 11 Perimeter and Area 
Chapter 12 
CBSE NCERT solutions for class 7 maths chapter 12 Algebraic Expressions 
Chapter 13 
NCERT solutions for class 7 maths chapter 13 Exponents and Powers 
Chapter 14 
NCERT Solutions for Class 7 Subjectwise
Some important properties and formulas from NCERT solutions for class 7 maths chapter 13 exponents and powers
For any nonzero integers, a and b and whole numbers m and n it obey certain properties given below
Tip If you understood the fundamental of this chapter, you don't need to remember above these findings. You can simply derive these properties by the strong fundamentals of this chapter. You should try to solve all the NCERT questions including the practice questions given at the end of every topic. You can take help from the CBSE NCERT solutions for class 7 maths chapter 13 exponents and powers if you are facing difficulties while solving the problems.
Happy Reading!!!