CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers InText Questions and Answers are provided by experts in order to help students secure good marks in exams.

## Class 7 Maths NCERT Solutions Chapter 13 Exponents and Powers InText Questions

Try These (Page 250)

Question 1.

Write 172, 5642, and 6374 in an expanded form.

Solution:

172 = 1 × 100 + 7 × 10 + 2

= 1 × 10^{2} + 7 × 10 + 2

5642 = 5 × 1000 + 6 × 100 + 4 × 10 + 2

= 5 × 10^{3} + 6 × 10^{2} + 4 × 10 + 2

6374 = 6 × 1000 + 3 × 100 + 7 × 10 + 4

= 6 × 10^{3} + 3 × 10^{2} + 7 × 10 + 4

Try These (Page 250)

Question 1.

Find five more such examples, where a number is expressed in exponential form. Also, identify the base and the exponent in each case.

Solution:

(i) 3^{4} = 3 × 3 × 3 × 3 = 81

In 3^{4}, 3 is known as base and 4 as an exponent.

(ii) 4^{4} = 4 × 4 × 4 × 4 = 256

In 4^{4}, 4 is known as base and 4 as an exponent.

(iii) 7^{5} = 7 × 7 × 7 × 7 × 7 = 16807

In 7^{5}, 7 is known as base and 5 as an exponent.

(iv) 5^{3} = 5 × 5 × 5 = 125

In 5^{3}, 5 is known as base and 3 as an exponent.

(v) 2^{6} = 2 × 2 × 2 × 2 × 2 × 2 = 64

In 2^{6},2 is known as base and 6 as an exponent.

Try These (Page 251)

Question 1.

(i) 729 as a power of 3

Solution:

We have

∴ 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3^{6}

(ii) 128 as a power of 2

Solution:

We have

∴ 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{7}

(iii) 343 as a power of 7.

Solution:

(iii) We have

∴ 343 = 7 × 7 × 7 = 7^{3}

Try These (Page 254)

Question 1.

Simplify and write in exponential form :

(i) 2^{5} × 2^{3}

Solution:

2^{5} × 2^{3} = 2^{5} + 3 = 2^{8}

(ii) p^{3} x p^{2}

Solution:

p^{3} × p^{2} = p^{3} + 2 = p^{5}

(iii) 4^{3} × 4^{2}

Solution:

4^{3} × 4^{2} = 4^{3} + 2 = 4^{5}

(iv) a^{3} × a^{2} × a^{7}

Solution:

a^{3} × a^{2} × a^{7} = a^{3+2+7} = a^{12}

(v) 5^{3} × 5^{7} × 5^{12}

Solution:

5^{3} × 5^{7} × 5^{12} = 5^{3+7+12} = 5^{22}

(vi) (- 4)^{100} × (- 4)^{20}

Solution:

(- 4)^{100} × (- 4)^{20} = (- 4)^{100+20} = (- 4)^{120}

Try These (Page 255)

Question 1.

Simplify and write in exponential form : (e.g.,11^{6} ÷ 11^{2} = 11^{4})

(i) 2^{9} ÷ 2^{3}

Solution:

2^{9} ÷ 2^{3} = 2^{9-3} = 2^{6}

(ii) 10^{8} ÷ 10^{4}

Solution:

10^{8} ÷ 10^{4} = 10^{8-4} =10^{4}

(iii) 9^{11} ÷ 9^{7}

Solution:

9^{11} ÷ 9^{7} = 9^{11-7} = 9^{4}

(iv) 20^{15} ÷ 20^{13}

Solution:

20^{15} ÷ 20^{13} = 20^{15-13} = 20^{2}

(v) 7^{13} ÷ 7^{10}

Solution:

7^{13} ÷ 7^{10} = 7^{13-10} = 7^{3}

Try These (Page 255)

Question 1.

Simplify and write the answer in exponential form:

(i) (6^{2})^{4}

Solution:

(6^{2})^{4} = 6^{2×4} = 6^{8}

(ii) (2^{2})^{100}

Solution:

(2^{2})^{100} = 2^{2×100} = 2^{200}

(iii) (7^{50})^{2}

Solution:

(7^{50})^{2} = 7^{50×2} = 7^{100}

(iv) (5^{3})^{7}

Solution:

(5^{3})^{7} = 5^{3×7} = 5^{21}

Try These (Page 256)

Question 1.

Put into another form using a^{m} × b^{m} = (ab)^{m} :

(i) 4^{3} × 2^{3}

Solution:

4^{3} × 2^{3} = (4 × 4 × 4) × (2 × 2 × 2)

= (4 × 2) × (4 × 2) × (4 × 2)

= (4 × 2)^{3}

(ii) 2^{5} × 6^{5}

Solution:

2^{5} × 6^{5} = (2 × 2 × 2 × 2 × 2) × (b × b × b × b × b)

= (2 × b) × (2 × b) × (2 × b) × (2 × b) × (2 × b)

= (2 × b)^{5} = (2b)^{5}

(iii) a^{2} × t^{2}

Solution:

a^{2} × t^{2} = (a × a) × (t × t) = (a × t) × (a × t)

=(a × t)^{2} = (at)^{2}

(iv) 5^{6} × (- 2)^{6}

Solution:

5^{6} × (- 2)^{6} = (5 × 5 × 5 × 5 × 5 × 5 ) × (- 2 × – 2 × – 2 × – 2 × – 2 × – 2)

= (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2) × (5 × – 2)

= (5 × – 2)^{6}

(v) (-2)^{4} × (-3)^{4}

Solution:

(- 2)^{4} × (- 3)^{4} = (- 2 × – 2 × – 2 × – 2) × (- 3 × – 3 × – 3 × – 3)

= (- 2 × – 3) × (- 2 × – 3) × (- 2 × – 3) × (- 2 × – 3)

= (- 2 × – 3)^{4}

Try These (Page 257)

Put into another form using

(i)

Solution:

(ii)

Solution:

(iii)

Solution:

(iv)

Solution:

(v)

Solution:

Try These (Page 261)

Question 1.

Expand by expressing powers of 10 in the exponential form :

(i) 172

Solution:

172 = 1 × 100 + 7 × 10 + 2 × 1

= 1 × 10^{2} + 7 × 10^{1} + 2 × 10°

(ii) 5,643

Solution:

5643 = 5 × 1000 + 6 × 100 + 4 × 10 +3 × 1

= 5 × 10^{3} + 6 × 10^{2} + 4 × 10^{1} + 3 x 10°

(iii) 56,439

Solution:

56439 = 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9

= 5 × 10^{4} + 6 × 10^{3} +4 × 10^{2} + 3 × 10^{1} + 9 × 10°

(iv) 1,76,428

Solution:

176428 = 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8 × 1

= 1 × 10^{5} + 7 × 10^{4} + 6 × 10^{3} + 4 × 10^{2} + 2 × 10^{1} + 8 × 10°

Try These (Page 262)

Question 1.

The distance between Sun and Saturn is 1,433,500,000,000 m or 1.4335 × 10^{12} m. The distance between Saturn and Uranus is 1,439,000,000,000 m or 1.439 × 10^{12} m. The distance between Sun and Earth is 149,600,000,000 m or 1.496 × 10^{11} m. Can you tell which of the three distances is the smallest?

Solution:

Of the three given distances, the distance between Sun and Earth is the smallest.