Maths Class 7 Exponents & Powers Chapter 11 Exercise 11.1 Question Answer

Solutions For All Chapters Maths Class 7

Ex 11.1 Class 7 Maths Question 1.
1. Find the value of:

(i) 2⁶

(ii) 9³

(iii) 11²

(iv) 5⁴

Solution:

(i) 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64

(ii) 9³ = 9 × 9 × 9 = 729

(iii) 11² = 11 × 11 = 121

(iv) 5⁴ = 5 × 5 × 5 × 5 = 625

Ex 11.1 Class 7 Maths Question 2.
Express the following in exponential form:

(i) 6 × 6 × 6 × 6

(ii) t × t

(iii) b × b × b × b

(iv) 5 × 5 × 7 × 7 × 7

(v) 2 × 2 × a × a

(vi) a × a × a × c × c × c× c × d

Solution:

(i) 6 × 6 × 6 × 6 = 6³

(ii) t × t = t²

(iii) b × b × b × b = b⁴

(iv) 5 × 5× 7 × 7 × 7 = 5² × 7³ = 5² · 7³

(v) 2 × 2 × a × a = 2² × a² = 2² · a²

(vi) a × a ×a × c × c × c × c × d = a³ × c⁴ × d = a³ · c⁴ · d

Ex 11.1 Class 7 Maths Question 3.
Express each of the following numbers using exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Solution:

Ex 11.1 Class 7 Maths Question 4.
Identify the greater number, wherever possible, in each of the following?

(i) 4³ or 3⁴

(ii) 5³ or 3⁵

(iii) 2⁸ or 8²

(iv) 100² or 2¹⁰⁰

(v) 2¹⁰ or 10²

Solution:

(i) 4³ or 3⁴

4³ = 4 × 4 × 4 = 64,

3⁴ = 3 × 3 × 3 × 3 = 81

Since 81 > 64
∴ 34 is greater than 43.

(ii) 5³ or 3⁵

5³ = 5 × 5 × 5 = 125

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

Since 243 > 125
∴ 35 is greater than 53.

(iii) 2⁸ or 8²

2⁸ =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8² = 8 × 8 = 64

Since 256 > 64
∴ 28 is greater than 28.

(iv) 100² or 2¹⁰⁰

100² = 100 × 100 = 10000

2¹⁰⁰ = 2 × 2 × 2 × … 100 times

Here 2 × 2 × 2 ×2 × 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 2 = 214 = 16384
Since 16384 > 10,000
∴ 2100 is greater than 1002.

(v) 2¹⁰  or 10²

2¹⁰  = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

10² = 10 × 10 = 100

Since 1024 > 100
∴ 210 is greater than 102.

Ex 11.1 Class 7 Maths Question 5.
Express each of the following as the product of powers of their prime

(i) 648

(ii) 405

(iii) 540

(iv) 3600

Solution:

Ex 11.1 Class 7 Maths Question 6.
Simplify:

(i) 2 × 10³

(ii) 7² × 2²

(iii) 2³ × 5

(iv) 3 × 4⁴

(v) 0 × 10²

(vi) 5² × 3³

(vii) 2⁴  × 3²

(viii) 3² × 10⁴

Solution:

(i) 2 × 10³ = 2 × 10 × 10 × 10 = = 2000

(ii) 7² × 2² = = 7 × 7 × 2 × 2 = 196

(iii) 2³ × 5 = 2 × 2 × 2 × 5 = 40

(iv) 3 × 4⁴ = 3 × 4 × 4 × 4 × 4 = 768

(v) 0 × 10² = 0 × 10 × 10 = = 0

(vi) 5² × 3³ = 5 × 5 × 3 × 3 × 3 = 675

(vii) 2⁴ × 3² = 2 × 2 × 2 × 2 × 3 × 3 = 144

(viii) 3² × 10⁴ = 3 × 3 × 10 × 10 × 10 × 10 = 90000

Ex 11.1 Class 7 Maths Question 7.
Simplify:

(i) (-4)3

(ii) (-3) × (-2)³

(iii) (-3)² × (-5)²

(iv) (-2)³ × (-10)³

Solution:

(i) (-4)² = (-4) × (-4) × (-4) = -64 [∵ (-a)odd number = -a odd number]
(ii) (-3) × (-2)³ = (-3) × (-2) × (-2) × (-2)
= (-3) × (-8) = 24
(iii) (-3)² × (-5)² = [(-3) × (-5)]²
= 15² = 225 [∵ am × bm = (ab)m)
(iv) (-2)³ × (-10)³ = [(-2) × (-10)]³
= 20² = 8000 [∵ am × bm = (ab)m]

Ex 11.1 Class 7 Maths Question 8.
Compare the following:

(i) 2.7 × 10¹²; 1.5 × 10⁸

(ii) 4 × 10¹⁴; 3 × 10¹⁴

Solution: