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Edited By Ravindra Pindel | Updated on Feb 07, 2024 06:16 PM IST

**NCERT Solutions for Exponents And Powers Class 7 -** 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.

This Story also Contains

- NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers - Important Formulae
- NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers - Important Points
- NCERT Solutions for Maths Chapter 13 Exponents and Powers Class 7
- NCERT for Maths Chapter 13 Exponents and Powers class 7 Topic 13.2 Exponents
- NCERT Solutions for Maths Chapter 13 Exponents and Powers Class 7Exercise 13.1
- NCERT Solutions for Class 7th Math Chapter 13 Exponents and Powers Topic 13.3.1
- NCERT Solutions for Class 7th Math Chapter 13 Exponents and Powers Topic 13.3.2
- NCERT Solutions for Class 7th Math Chapter 13 Exponents and Powers Topic 13.3.3
- NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.4
- NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Topic 13.3.5
- NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.2
- NCERT Solutions for Chapter 13 Maths Class 7 Exponents and Powers Topic 13.6
- NCERT Solutions for Chapter 13 Maths Class 7 Exponents and Powers Exercise 13.3
- Exponents and Powers Class 7 Maths Chapter 13- Topics
- Some Important Properties and Formulas from 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 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.

a^{m} × a^{n} = a^{m+n}

a^{m} ÷ a^{n} = a^{m-n}

( a^{m} )^{n} = a^{mn}

a^{m} × b^{m} = (ab)^{m}

a^{m} ÷ b^{n} = (a÷b)^{m}

a^{0} = 1 ( a, non-zero integer)

(-)^{even number} = 1

(-)^{odd number} = -1

**Exponents: **Exponents represent repeated multiplication of a number (base) by itself.

x^{4} where x is the base and 4 is the exponent. It is read as x raised to the power of 4 or fourth power of x.

**Understanding Powers of 10:**

- Powers of 10 are commonly used in scientific notation and decimal places.
- 10
^{n}represents a 1 followed by 'n' zeros.

Free download **NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers PDF **for CBSE Exam.

** Question:(i) ** Express:

729 as a power of 3

** Answer: **

729 as a power of 3 is given as

** 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.

** Question:(i) ** Simplify and write in exponential form:

** Answer: **

can be simplified as

** 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

** 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

** 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

** 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

** 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 |

** 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

** 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.

(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.

** 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.

- 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

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | |

Chapter 9 | |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | Exponents and Powers |

Chapter 14 | |

Chapter 15 |

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 solution for class 7 maths chapter 13 exponents and powers if you are facing difficulties while solving the problems.

** Happy Reading!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

1. What is exponents?

Exponent is a method expressing large numbers in terms of powers.

For example; 2 multiplied 3 times i.e, 2×2×2 can be expressed as 2^3 so where 3 exponents of 2. To get deeper understanding of these concepts students can download exponents and powers class 7 pdf and study both onlline and offline mode. For Hindi students we are working to create class 7 hindi chapter 13 pdf which will be available soon.

2. What are the topics covered in NCERT Class 7 Maths Chapter13?

Here are the topics covered in NCERT Class 7 Maths chapter13

- 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

Hindi students can download class 7th hindi chapter 13 question answer pdf soon.

3. How many exercises in NCERT Class 7 Maths chapter 13?

There are 3 exercises in NCERT Class 7 Maths chapter 13

NCERT Exponents and Powers class 7 Exercise 13.1 - 8 Questions

NCERT Exponents and Powers class 7 Exercise 13.2 - 5 Questions

NCERT Exponents and Powers class 7 Exercise 13.3 - 4 Questions

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