# 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.

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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 NCERT. 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 NCERT Solutions for Class 7. Check NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get solutions to three exercises of this chapter.

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## 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

## 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

Question: 2 Express the following in exponential form:

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

(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?

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

(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(v iii) 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.

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.1

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

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.2

Question: 1 Simplify and write in exponential form: (eg., )

can be simplified as

can be simplified as

can be simplified as

can be simplified as

can be simplified as

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.3

Question: Simplify and write the answer in exponential form:

can be simplified as

can be simplified as

can be simplified as

can be simplified as

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.4

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

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.5

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

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.2

Question: 1 Using laws of exponents, simplify and write the answer in exponential form:

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:

can be simplified as

Question: 2(ii) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(iii) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(iv) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(v) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(vi) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(vii) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(viii) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(ix) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(x) Simplify and express each of the following in exponential form:

can be simplified as

Question: 2(xi) Simplify and express each of the following in exponential form:

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.

Question: 4 Express each of the following as a product of prime factors only in exponential form:

 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

Question: Expand by expressing powers of 10 in the exponential 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

## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.3

Question: 1 Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

(i) 279404

(ii) 3006194

(iii) 2806196

(IV) 120719

(V) 20068

Question: 2 Find the number from each of the following expanded forms:

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

(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.

(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.

## Exponents and Powers Class 7 Maths Chapter 13- Topics

• Exponents
• Laws Of Exponents
• Multiplying Powers With The Same Base
• Dividing Powers With The Same Base
• Taking Power Of A Power
• Multiplying Powers With The Same Exponents
• Dividing Powers With The Same Exponents
• Miscellaneous Examples Using The Laws Of Exponents
• Decimal Number System
• Expressing Large Numbers In The Standard Form

### NCERT Solutions for Class 7 Maths Chapter Wise

 Chapter No. Chapter Name Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangle and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes

### NCERT Solutions for Class 7 Subject Wise

 NCERT Solutions for Class 7 Maths NCERT Solutions for Class 7 Science

## 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.

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