NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 

NCERT Solutions for Class 7 Maths Chapter 13

NCERT Solutions for Class 7 Maths Chapter 13: NCERT Solutions for Class 7 Maths Chapter 13 provide detailed explanations and answers to the exercises in the chapter on Exponents and Powers. With these solutions students can strengthen their understanding of the concepts and improve their problem-solving skills. Practicing with NCERT Solutions for Chapter 13 will help students prepare thoroughly for exams and build a strong foundation in mathematics.

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NCERT Solutions for Class 7 Maths Chapter 13 PDF

NCERT Solutions for Class 7 Maths Chapter 13 PDF

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

Exercise 13.1 Page: 252

1. Find the value of:

(i) 2 ⁶

Solution:-

(ii) 9 ³

Solution:-

(iii) 11 ²

Solution:-

(iv) 5 ⁴

Solution:-

2. Express the following in exponential form:

(i) 6 × 6 × 6 × 6

Solution:-

(ii) t × t

Solution:-

(iii) b × b × b × b

Solution:-

(iv) 5 × 5× 7 × 7 × 7

Solution:-

(v) 2 × 2 × a × a

Solution:-

(vi) a × a × a × c × c × c × c × d

Solution:-

3. Express each of the following numbers using the exponential notation:

(i) 512

Solution:-

(ii) 343

Solution:-

(iii) 729

Solution:-

(iv) 3125

Solution:-

4. Identify the greater number, wherever possible, in each of the following.

(i) 4 ³ or 3 ⁴

Solution:-

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(ii) 5 ³ or 3 ⁵

Solution:-

(iii) 2 ⁸ or 8 ²

Solution:-

(iv) 100 ² or 2 ¹⁰⁰

Solution:-

(v) 2 ¹⁰ or 10 ²

Solution:-

5. Express each of the following as a product of powers of their prime factors:

(i) 648

Solution:-

(ii) 405

Solution:-

(iii) 540

Solution:-

(iv) 3,600

Solution:-

6. Simplify:

(i) 2 × 10 ³

Solution:-

(ii) 7 ² × 2 ²

Solution:-

(iii) 2 ³ × 5

Solution:-

(iv) 3 × 4 ⁴

Solution:-

(v) 0 × 10 ²

Solution:-

(vi) 5 ² × 3 ³

Solution:-

(vii) 2 ⁴ × 3 ²

Solution:-

(viii) 3 ² × 10 ⁴

Solution:-

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7. Simplify:

(i) (– 4) ³

Solution:-

(ii) (–3) × (–2) ³

Solution:-

(iii) (–3) ² × (–5) ²

Solution:-

(iv) (–2) ³ × (–10) ³

Solution:-

8. Compare the following numbers:

(i) 2.7 × 10 ¹² ; 1.5 × 10 ⁸

Solution:-

(ii) 4 × 10 ¹⁴ ; 3 × 10 ¹⁷

Solution:-

Exercise 13.2 Page: 260

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

(i) 3 ² × 3 ⁴ × 3 ⁸

Solution:-

(ii) 6 ¹⁵ ÷ 6 ¹⁰

Solution:-

(iii) a ³ × a ²

Solution:-

(iv) 7 ^x × 7 ²

Solution:-

(v) (5 ² ) ³ ÷ 5 ³

Solution:-

(vi) 2 ⁵ × 5 ⁵

Solution:-

(vii) a ⁴ × b ⁴

Solution:-

(viii) (3 ⁴ ) ³

Solution:-

(ix) (2 ²⁰ ÷ 2 ¹⁵ ) × 2 ³

Solution:-

(x) 8 ^t ÷ 8 ²

Solution:-

2. Simplify and express each of the following in exponential form:

(i) (2 ³ × 3 ⁴ × 4)/ (3 × 32)

Solution:-

(ii) ((5 ² ) ³ × 5 ⁴ ) ÷ 5 ⁷

Solution:-

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(iii) 25 ⁴ ÷ 5 ³

Solution:-

(iv) (3 × 7 ² × 11 ⁸ )/ (21 × 11 ³ )

Solution:-

(v) 3 ⁷ / (3 ⁴ × 3 ³ )

Solution:-

(vi) 2 ⁰ + 3 ⁰ + 4 ⁰

Solution:-

(vii) 2 ⁰ × 3 ⁰ × 4 ⁰

Solution:-

(viii) (3 ⁰ + 2 ⁰ ) × 5 ⁰

Solution:-

(ix) (2 ⁸ × a ⁵ )/ (4 ³ × a ³ )

Solution:-

(x) (a ⁵ /a ³ ) × a ⁸

Solution:-

(xi) (4 ⁵ × a ⁸ b ³ )/ (4 ⁵ × a ⁵ b ² )

Solution:-

(xii) (2 ³ × 2) ²

Solution:-

3. Say true or false and justify your answer:

(i) 10 × 10 ¹¹ = 100 ¹¹

Solution:-

(ii) 2 ³ > 5 ²

Solution:-

(iii) 2 ³ × 3 ² = 6 ⁵

Solution:-

(iv) 3 ⁰ = (1000) ⁰

Solution:-

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

(i) 108 × 192

Solution:-

(ii) 270

Solution:-

(iii) 729 × 64

(iv) 768

Solution:-

5. Simplify:

(i) ((2 ⁵ ) ² × 7 ³ )/ (8 ³ × 7)

Solution:-

(ii) (25 × 5 ² × t ⁸ )/ (10 ³ × t ⁴ )

Solution:-

(iii) (3 ⁵ × 10 ⁵ × 25)/ (5 ⁷ × 6 ⁵ )

Solution:-

1. Write the following numbers in the expanded forms:

(a) 279404

Solution:-

(b) 3006194

Solution:-

(c) 2806196

Solution:-

(d) 120719

Solution:-

(e) 20068

Solution:-

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

(a) (8 × 10) ⁴ + (6 × 10) ³ + (0 × 10) ² + (4 × 10) ¹ + (5 × 10) ⁰

Solution:-

(b) (4 × 10) ⁵ + (5 × 10) ³ + (3 × 10) ² + (2 × 10) ⁰

Solution:-

(c) (3 × 10) ⁴ + (7 × 10) ² + (5 × 10) ⁰

Solution:-

(d) (9 × 10) ⁵ + (2 × 10) ² + (3 × 10) ¹

Solution:-

3. Express the following numbers in standard form:

(i) 5,00,00,000

Solution:-

(ii) 70,00,000

Solution:-

(iii) 3,18,65,00,000

Solution:-

(iv) 3,90,878

Solution:-

(v) 39087.8

Solution:-

(vi) 3908.78

Solution:-

4. Express the number appearing in the following statements in standard form.

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

Solution:-

(b) Speed of light in a vacuum is 300,000,000 m/s.

Solution:-

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

Solution:-

(d) Diameter of the Sun is 1,400,000,000 m.

Solution:-

(e) In a galaxy, there are, on average, 100,000,000,000 stars.

Solution:-

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

Solution:-

(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.

Solution:-

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

Solution:-

(i) The Earth has 1,353,000,000 cubic km of seawater.

Solution:-

(j) The population of India was about 1,027,000,000 in March 2001.

Solution:-