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

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 × 10² + 7 × 10 + 2

5642 = 5 × 1000 + 6 × 100 + 4 × 10 + 2
= 5 × 10³ + 6 × 10² + 4 × 10 + 2

6374 = 6 × 1000 + 3 × 100 + 7 × 10 + 4
= 6 × 10³ + 3 × 10² + 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) 3⁴ = 3 × 3 × 3 × 3 = 81
In 3⁴, 3 is known as base and 4 as an exponent.
(ii) 4⁴ = 4 × 4 × 4 × 4 = 256
In 4⁴, 4 is known as base and 4 as an exponent.
(iii) 7⁵ = 7 × 7 × 7 × 7 × 7 = 16807
In 7⁵, 7 is known as base and 5 as an exponent.
(iv) 5³ = 5 × 5 × 5 = 125
In 5³, 5 is known as base and 3 as an exponent.
(v) 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
In 2⁶,2 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 = 3⁶

(ii) 128 as a power of 2
Solution:
We have

∴ 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷

(iii) 343 as a power of 7.
Solution:
(iii) We have

∴ 343 = 7 × 7 × 7 = 7³

Try These (Page 254)

Question 1.
Simplify and write in exponential form :
(i) 2⁵ × 2³
Solution:
2⁵ × 2³ = 2⁵ + 3 = 2⁸

(ii) p³ x p²
Solution:
p³ × p² = p³ + 2 = p⁵

(iii) 4³ × 4²
Solution:
4³ × 4² = 4³ + 2 = 4⁵

(iv) a³ × a² × a⁷
Solution:
a³ × a² × a⁷ = a³⁺²⁺⁷ = a¹²

(v) 5³ × 5⁷ × 5¹²
Solution:
5³ × 5⁷ × 5¹² = 5³⁺⁷⁺¹² = 5²²

(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.,11⁶ ÷ 11² = 11⁴)
(i) 2⁹ ÷ 2³
Solution:
2⁹ ÷ 2³ = 2^9-3 = 2⁶

(ii) 10⁸ ÷ 10⁴
Solution:
10⁸ ÷ 10⁴ = 10^8-4 =10⁴

(iii) 9¹¹ ÷ 9⁷
Solution:
9¹¹ ÷ 9⁷ = 9^11-7 = 9⁴

(iv) 20¹⁵ ÷ 20¹³
Solution:
20¹⁵ ÷ 20¹³ = 20^15-13 = 20²

(v) 7¹³ ÷ 7¹⁰
Solution:
7¹³ ÷ 7¹⁰ = 7^13-10 = 7³

Try These (Page 255)

Question 1.
Simplify and write the answer in exponential form:
(i) (6²)⁴
Solution:
(6²)⁴ = 6^2×4 = 6⁸

(ii) (2²)¹⁰⁰
Solution:
(2²)¹⁰⁰ = 2^2×100 = 2²⁰⁰

(iii) (7⁵⁰)²
Solution:
(7⁵⁰)² = 7^50×2 = 7¹⁰⁰

(iv) (5³)⁷
Solution:
(5³)⁷ = 5^3×7 = 5²¹

Try These (Page 256)

Question 1.
Put into another form using a^m × b^m = (ab)^m :
(i) 4³ × 2³
Solution:
4³ × 2³ = (4 × 4 × 4) × (2 × 2 × 2)
= (4 × 2) × (4 × 2) × (4 × 2)
= (4 × 2)³

(ii) 2⁵ × 6⁵
Solution:
2⁵ × 6⁵ = (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) a² × t²
Solution:
a² × t² = (a × a) × (t × t) = (a × t) × (a × t)
=(a × t)² = (at)²

(iv) 5⁶ × (- 2)⁶
Solution:
5⁶ × (- 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 × 10² + 7 × 10¹ + 2 × 10°

(ii) 5,643
Solution:
5643 = 5 × 1000 + 6 × 100 + 4 × 10 +3 × 1
= 5 × 10³ + 6 × 10² + 4 × 10¹ + 3 x 10°

(iii) 56,439
Solution:
56439 = 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9
= 5 × 10⁴ + 6 × 10³ +4 × 10² + 3 × 10¹ + 9 × 10°

(iv) 1,76,428
Solution:
176428 = 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8 × 1
= 1 × 10⁵ + 7 × 10⁴ + 6 × 10³ + 4 × 10² + 2 × 10¹ + 8 × 10°

Try These (Page 262)

Question 1.
The distance between Sun and Saturn is 1,433,500,000,000 m or 1.4335 × 10¹² m. The distance between Saturn and Uranus is 1,439,000,000,000 m or 1.439 × 10¹² m. The distance between Sun and Earth is 149,600,000,000 m or 1.496 × 10¹¹ 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.