# 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 step-by-step 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.

Exercise:13.1

Exercise:13.2

Exercise:13.3

## 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

## Solutions of NCERT for class 7 maths chapter 13 exponents and powers topic 13.2 exponents

Question:(i) Express:

729 as a power of 3

729 as a power of 3 is given as

Question:(ii) Express:

128 as a power of 2

128 as a power of 2 can be given as

Question:(iii) Express:

343 as a power of 7

343 as a power of 7 can be givena as

CBSE NCERT solutions for class 7 maths chapter 13 exponents and powers-Exercise: 13.1

Question:1(i) Find the value of:

the value of  is given by

Question:1(ii)Find the value of:

the value of  is given by

Question:1(iii) Find the value of:

the value of   is given by

Question:1(iv) Find the value of:

the value of  is given by

can be given as

.

can be given as .

can be given as .

can be given as

.

can be given as

.

can be given as

(i) 512    (ii) 343    (iii) 729    (iv) 3125

(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

since

is greater than

since

is greater than

since

is greater than

since

is greater than

since

is greater than

(i) 648    (ii) 405    (iii) 540   (iv) 3,600

(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:

can be simplified as

Question:6(ii) Simplify:

can be simplified as

Question:6(iii) Simplify:

can be simplified as

Question:6(iv) Simplify:

can be simplified as

Question:6(v) Simplify:

can be simplified as

Question:6(vi) Simplify:

can be simplified as

Question:6(vii) Simplify:

can be simplified as

Question:6(viii) Simplify:

can be simplified as

Question:7(i) Simplify:

can be simplified as

Question:7(ii) Simplify:

can be simplified as

Question:7(iii) Simplify:

can be simplified as

Question:7(iv) Simplify:

can be simplified as

Question:8 Compare the following numbers:

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:

can be simplified as

Question:(ii) Simplify and write in exponential form:

can be simplified as

Question:(iii) Simplify and write in exponential form:

can be simplified as

Question:(iv) Simplify and write in exponential form:

can be simplified as

Question:(v)  Simplify and write in exponential form:

can be simplified as

Question:(vi) Simplify and write in exponential form:

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

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

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 :

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 :

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 powers-Exercise: 13.2

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

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(xii) Simplify and express each of the following in exponential form:

can be simplified as

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.

 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

Question:5(i) Simplify:

can be simplified as

Question:5(ii) Simplify:

can be simplified as

Question:5(iii) Simplify:

can be simplified as

## NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.6 expressing large numbers in the standard form

(i) 172      (ii) 5,643    (iii) 56,439    (iv) 1,76,428

(i) 172

(ii) 5,643

(iii) 56,439

(iv) 1,76,428

Solutions of NCERT for class 7 maths chapter 13 exponents and powers-Exercise: 13.3

279404, 3006194, 2806196, 120719, 20068

(i)  279404

(ii) 3006194

(iii) 2806196

(IV)  120719

(V)  20068

Thus, the above problems are simplified in simpler forms.

(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

(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

(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.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 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.

(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.

(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- Chapter-wise

 Chapter No. Chapter Name Chapter 1 Solutions of NCERT for class 7 maths chapter 1 Integers Chapter 2 CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals Chapter 3 NCERT solutions for class 7 maths chapter 3 Data Handling 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 Solutions of NCERT for class 7 maths chapter 14 Symmetry

## NCERT Solutions for Class 7- Subject-wise

Some important properties and formulas from NCERT solutions for class 7 maths chapter 13 exponents and powers-

For any non-zero 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.