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# NCERT solutions for Class 7 Mathematics chapter 13 - Exponents and Powers

## Chapter 13: Exponents and Powers

Ex. 13.10Ex. 13.20Ex. 13.30Others

#### Chapter 13: Exponents and Powers Exercise 13.10 solutions [Pages 252 - 253]

Ex. 13.10 | Q 1.1 | Page 252

Find the value of:26

Ex. 13.10 | Q 1.2 | Page 252

Find the value of:93

Ex. 13.10 | Q 1.3 | Page 252

Find the value of: 112

Ex. 13.10 | Q 1.4 | Page 252

Find the value of: 54

Ex. 13.10 | Q 2.1 | Page 252

Express the given in exponential form:

6 × 6 × 6 × 6

Ex. 13.10 | Q 2.2 | Page 252

Express the given in exponential form:

t × t

Ex. 13.10 | Q 2.3 | Page 252

Express the given in exponential form:

b × b × b × b

Ex. 13.10 | Q 2.4 | Page 252

Express the given in exponential form:

5 × 5 × 7 ×7 × 7

Ex. 13.10 | Q 2.5 | Page 252

Express the given in exponential form:

2 × 2 × a × a

Ex. 13.10 | Q 2.6 | Page 252

Express the given in exponential form:

a × a × a × c × c × c × c × d

Ex. 13.10 | Q 3.1 | Page 253

Express the numbers using exponential notation:

512

Ex. 13.10 | Q 3.2 | Page 253

Express the numbers using exponential notation:

343

Ex. 13.10 | Q 3.3 | Page 253

Express the numbers using exponential notation:

729

Ex. 13.10 | Q 3.4 | Page 253

Express the numbers using exponential notation:

3125

Ex. 13.10 | Q 4.1 | Page 253

Identify the greater number, wherever possible, in the following?

43 or 34

Ex. 13.10 | Q 4.2 | Page 253

Identify the greater number, wherever possible, in the following?

53 or 35

Ex. 13.10 | Q 4.3 | Page 253

Identify the greater number, wherever possible, in the following?

28 or 82

Ex. 13.10 | Q 4.4 | Page 253

Identify the greater number, wherever possible, in the following?

100or 2100

Ex. 13.10 | Q 4.5 | Page 253

Identify the greater number, wherever possible, in the following?

210 or 102

Ex. 13.10 | Q 5.1 | Page 253

Express the following as product of powers of their prime factors:

648

Ex. 13.10 | Q 5.2 | Page 253

Express the following as product of powers of their prime factors:

405

Ex. 13.10 | Q 5.3 | Page 253

Express the following as product of powers of their prime factors:

540

Ex. 13.10 | Q 5.4 | Page 253

Express the following as product of powers of their prime factors:

3,600

Ex. 13.10 | Q 6.1 | Page 253

Simplify : 2 × 103

Ex. 13.10 | Q 6.2 | Page 253

Simplify: 72 × 22

Ex. 13.10 | Q 6.3 | Page 253

Simplify: 23 × 5

Ex. 13.10 | Q 6.4 | Page 253

Simplify : 3 × 44

Ex. 13.10 | Q 6.5 | Page 253

Simplify: 0 × 102 ­­­­

Ex. 13.10 | Q 6.6 | Page 253

Simplify: 52 × 33

Ex. 13.10 | Q 6.7 | Page 253

Simplify:2× 32

Ex. 13.10 | Q 6.8 | Page 253

Simplify: 32 × 104

Ex. 13.10 | Q 7.1 | Page 253

Simplify: (− 4)3

Ex. 13.10 | Q 7.2 | Page 253

Simplify: (− 3) × (− 2)3

Ex. 13.10 | Q 7.3 | Page 253

Simplify: (− 3)2 × (− 5)2

Ex. 13.10 | Q 7.4 | Page 253

Simplify: (− 2)3 × (−10)3

Ex. 13.10 | Q 8.1 | Page 253

Compare the Given numbers:

2.7 × 1012; 1.5 × 108

Ex. 13.10 | Q 8.2 | Page 253

Compare the Given numbers:

4 × 1014; 3 × 1017

#### Chapter 13: Exponents and Powers Exercise 13.20 solutions [Pages 260 - 261]

Ex. 13.20 | Q 1.01 | Page 260

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

32 × 34 × 38

Ex. 13.20 | Q 1.02 | Page 260

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

615 ÷ 610

Ex. 13.20 | Q 1.03 | Page 260

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

a3 × a2

Ex. 13.20 | Q 1.04 | Page 260

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

7x× 72

Ex. 13.20 | Q 1.05 | Page 260

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

(5^2)^3 ÷ 5^3

Ex. 13.20 | Q 1.06 | Page 260

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

25 × 55

Ex. 13.20 | Q 1.07 | Page 260

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

a4 × b4

Ex. 13.20 | Q 1.08 | Page 260

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

(34)3

Ex. 13.20 | Q 1.09 | Page 260

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

(2^20 ÷ 2^15) xx 2^3

Ex. 13.20 | Q 1.1 | Page 260

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

8t ÷ 82

Ex. 13.20 | Q 2.01 | Page 260

Simplify and express the following in exponential form:

(2^3 xx 3^4 xx 4)/(3 xx 32)

Ex. 13.20 | Q 2.02 | Page 260

Simplify and express the following in exponential form:

((52 )3 × 54 )÷ 57

Ex. 13.20 | Q 2.03 | Page 260

Simplify and express the following in exponential form:

254 ÷53

Ex. 13.20 | Q 2.04 | Page 260

Simplify and express the following in exponential form:

(3 xx 7^2 xx 11^8)/(21 xx 11^3)

Ex. 13.20 | Q 2.05 | Page 260

Simplify and express the following in exponential form:

3^7/(3^4 xx 3^3)

Ex. 13.20 | Q 2.06 | Page 260

Simplify and express the following in exponential form:

20 + 30 + 40

Ex. 13.20 | Q 2.07 | Page 260

Simplify and express the following in exponential form:

20 × 30 × 40

Ex. 13.20 | Q 2.08 | Page 260

Simplify and express the following in exponential form:

(30 + 20) × 50

Ex. 13.20 | Q 2.09 | Page 260

Simplify and express the following in exponential form:

(2^8 xxa^5)/(4^3 xx a^3)

Ex. 13.20 | Q 2.1 | Page 260

Simplify and express the following in exponential form

(a^5/a^3)  xx a^8

Ex. 13.20 | Q 2.11 | Page 260

Simplify and express the following in exponential form

(4^5 xx a^8b^3)/(4^5 xx a^5b^2)

Ex. 13.20 | Q 2.12 | Page 260

Simplify and express the following in exponential form:

(2^3 xx 2)^2

Ex. 13.20 | Q 3.1 | Page 260

10 × 1011 = 10011

Ex. 13.20 | Q 3.2 | Page 260

23 > 52

Ex. 13.20 | Q 3.3 | Page 260

23 × 32 = 65

Ex. 13.20 | Q 3.4 | Page 260

30 = (1000)0

Ex. 13.20 | Q 4.1 | Page 261

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

108 × 192

Ex. 13.20 | Q 4.2 | Page 261

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

270

Ex. 13.20 | Q 4.3 | Page 261

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

729 × 64

Ex. 13.20 | Q 4.4 | Page 261

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

768

Ex. 13.20 | Q 5.1 | Page 261

Simplify: ((2^5)^2 xx 7^3)/(8^3 xx 7)

Ex. 13.20 | Q 5.2 | Page 261

Simplify: (25 xx 5^2 xx t^8)/(10^3 xx t^4)

Ex. 13.20 | Q 5.3 | Page 261

Simplify: (3^5 xx 10^5 xx 25)/(5^7 xx 6^5)

#### Chapter 13: Exponents and Powers Exercise 13.20, 13.30 solutions [Page 263]

Ex. 13.20 | Q 1 | Page 263

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Ex. 13.20 | Q 2.1 | Page 263

Find the number from the following expanded forms:

8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100

Ex. 13.20 | Q 2.2 | Page 263

Find the number from the following expanded forms:

4 × 10+ 5 × 10+ 3 × 10+ 2 × 100

Ex. 13.20 | Q 2.3 | Page 263

Find the number from the following expanded forms:

3 × 104 + 7 × 102 + 5 × 100

Ex. 13.20 | Q 2.4 | Page 263

Find the number from the following expanded forms:

9 × 105 + 2 × 102 + 3 × 101

Ex. 13.30 | Q 3.1 | Page 263

Express the given numbers in standard form:

5, 00, 00, 000

Ex. 13.20 | Q 3.2 | Page 263

Express the given numbers in standard form:

70, 00, 000

Ex. 13.20 | Q 3.3 | Page 263

Express the given numbers in standard form:

3, 18, 65, 00, 000

Ex. 13.20 | Q 3.4 | Page 263

Express the given numbers in standard form:

3, 90, 878

Ex. 13.20 | Q 3.5 | Page 263

Express the given numbers in standard form:

39087.8

Ex. 13.20 | Q 3.6 | Page 263

Express the given numbers in standard form:

3908.78

Q 4.01 | Page 263

Express the number appearing in the given statements in standard form

The distance between Earth and Moon is 384, 000, 000 m.

Q 4.02 | Page 263

Express the number appearing in the given statements in standard form

Speed of light in vacuum is 300, 000, 000 m/s.

Q 4.03 | Page 263

Express the number appearing in the given statements in standard form

Diameter of the Earth is 1, 27, 56, 000 m.

Q 4.04 | Page 263

Express the number appearing in the given statements in standard form

Diameter of the Sun is 1, 400, 000, 000 m.

Q 4.05 | Page 263

Express the number appearing in the given statements in standard form

In a galaxy there are on an average 100, 000, 000, 000 stars.

Q 4.06 | Page 263

Express the number appearing in the given statements in standard form

The universe is estimated to be about 12, 000, 000, 000 years old.

Q 4.07 | Page 263

Express the number appearing in the given statements in standard form

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.

Q 4.08 | Page 263

Express the number appearing in the given statements in standard form

60, 230, 000, 000, 000, 000, 000, 000 molecules are contained in a drop of water weighing 1.8 gm.

Q 4.09 | Page 263

Express the number appearing in the given statements in standard form

The earth has 1, 353, 000, 000 cubic km of sea water.

Q 4.1 | Page 263

Express the number appearing in the given statements in standard form

The population of India was about 1, 027, 000, 000 in March, 2001

## Chapter 13: Exponents and Powers

Ex. 13.10Ex. 13.20Ex. 13.30Others

## NCERT solutions for Class 7 Mathematics chapter 13 - Exponents and Powers

NCERT solutions for Class 7 Maths chapter 13 (Exponents and Powers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 7 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 7 Mathematics chapter 13 Exponents and Powers are Concept 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.

Using NCERT Class 7 solutions Exponents and Powers exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 7 prefer NCERT Textbook Solutions to score more in exam.

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