Well-designed AP 7th Class Maths Textbook Solutions Chapter 11 Exponents and Powers Exercise 11.1 offers step-by-step explanations to help students understand problem-solving strategies.

## Exponents and Powers Class 7 Exercise 11.1 Solutions – 7th Class Maths 11.1 Exercise Solutions

Question 1.

1. Find the value of :

i) 2^{6}

Solution:

2^{6} = 2 × 2 × 2 × 2 × 2 × 2 = 64

ii) 9^{3}

Solution:

9^{3} = 9 × 9 × 9 = 81 × 9 = 729

iii) 11^{2}

Solution:

11^{2} = 11 × 11 = 121

iv) 5^{4}

Solution:

5^{4} = 5 × 5 × 5 × 5 = 25 × 25 = 625

Question 2.

Express the following in exponential form :

i) 6 × 6 × 6 × 6

Solution:

6 × 6 × 6 × 6 = 6^{4}

ii) t × t

Solution:

t × t = t^{2}

iii) b × b × b × b

Solution:

b × b × b × b = b^{4}

iv) 5 × 5 × 7 × 7 × 7

Solution:

5 × 5 × 7 × 7 × 7 = 5^{2} × 7^{3}

v) 2 × 2 × a × a

Solution:

2 × 2 × a × a = 2^{2} × a^{2}

vi) a × a × a × c × c × c × c × d

Solution:

a × a × a × c × c × c × c × d = a^{3} × c^{1} × d

Question 3.

Express each of the following numbers using exponential notation :

i) 512

Solution:

512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

512 = 2^{9}

ii) 343

Solution:

343

343 = 7 × 7 × 7

343 = 7^{3}

iii) 729

Solution:

729

729 = 3 × 3 × 3 × 3 × 3 × 3

729 = 3^{6}

iv) 3125

Solution:

3125

3125 = 5 × 5 × 5 × 5 × 5 = 5^{5}

Question 4.

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

i) 4^{3} or 3^{4}

Solution:

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

= 2^{6} or 3^{4} = 64 or 81

81 > 64

∴ 3^{4} > 4^{3}

ii) 5^{3} or 3^{5}

Solution:

5^{3} or 3^{5}

5^{3} = 5 × 5 × 5 = 125

3^{5} = 3 × 3 × 3 × 3 × 3 = 243

∴ 3^{5} > 5^{3}

iii) 2^{8} or 8^{2}

Solution:

2^{8} or 8^{2}

2^{8} = (2^{4})^{2} = 16^{2} = 256

8^{2} = 8 × 8 = 64

256 > 64

∴ 2^{8} > 8^{2}

iv) 100^{2} or 2^{100}

Solution:

100^{2} or 2^{100}

(10^{2})^{2} or 2^{100}

10^{4} or 2^{100}

10,000 or (2^{10})^{10}

10,000 or (1024)^{10}

∴ 2^{100} >100^{2}

v) 2^{10}or 10^{2}

Solution:

2^{10} or 10^{2}

2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

10^{2} = 100

1024 > 100

∴ 2^{10} > 10^{2}

Question 5.

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

i) 648

Solution:

648

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

648 = 2^{3} × 3^{4}

ii) 405

Solution:

405

405 = 5 × 3 × 3 × 3 × 3

405 = 5 × 3^{4}

iii) 540

Solution:

540

540 = 2 × 2 × 5 × 3 × 3 × 3

540 = 2^{2} × 5 × 3^{3}

iv) 3,600

Solution:

3,600

3600 = 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3

3600 = 2^{4} × 5^{2} × 3^{3}

Question 6.

Simplify :

i) 2 × 10^{3}

Solution:

2 × 10^{3} = 2 × 1000 = 2000

ii) 7^{2} × 2^{2}

Solution:

7^{2} × 2^{2} = (7 × 2)^{2} [∵ a^{m} × b^{m} = (ab)^{m}]

= 14^{2} = 14 × 14 = 196

iii) 2^{3} × 5

Solution:

2^{3} × 5 = 8 × 4 = 40

iv) 3 × 4^{4}

Solution:

3 × 4^{4} = 3 × 256 = 768

v) 0 × 10^{2}

Solution:

0 × 10^{2} = 0 × 100 = 0

vi) 5^{2} × 3^{3}

Solution:

5^{2} × 3^{3} = 25 × 27 = 675

vii) 2^{4} × 3^{2}

Solution:

2^{4} × 3^{2} = 16 × 9 = 144

viii) 3^{2} × 10^{4}

Solution:

3^{2} × 10^{4} = 9 × 10000 = 90,000

Question 7.

Simplify :

i) (-4)^{3}

Solution:

(-4)^{3} = -4× -4 × -4 = -64

ii) (-3) × (-2)^{3}

Solution:

(-3) × (-2)^{3} = -3 × -8 = 24

iii) (-3)^{2} × (-5)^{2}

Solution:

(-3)^{2} × (-5)^{2} = 9 × 25 = 225

(OR)

(-3)^{2} × (-5)^{2} = (-3 × -5)^{2}

∵ a^{m} × b^{m} = (a × b)^{m}

= (15)^{2} = 15 × 15 = 225

iv) (-2)^{3} × (-10)^{3}

Solution:

(-2)^{3} × (-10)^{3} = -8 × -1000 = 8000

(OR)

(-2)^{3} × (-10)^{3} =(-2 × -10)^{3}

∵ a^{m} × b^{m} = (a × b)^{m}

= (20)^{2}

= 20 × 20 × 20 = 8000

Question 8.

Compare the following numbers :

i) 2.7 × 10^{12}; 1.5 × 10^{5}

Solution:

2.7 × 10^{12} = \(\frac{27}{10^1}\) × 10^{12}

= 27 × 10^{12-1}

∵ \(\frac{a^m}{a^n}\) = a^{m-n}

= 27 × 10^{11}

1.5 × 10^{8} = \(\frac{15}{10^1}\) × 10^{8}

= 15 × 10^{8 – 1}

∵ \(\frac{a^m}{a^n}\) = a^{m-n}

= 15 × 10^{7}

∴ 2.7 × 10^{11} > 1.5 × 10^{7}

2.7 × 10^{12} > 1.5 × 10^{8}

ii) 4 × 10^{14} ; 3 × 10^{17}

Solution:

4 × 10^{14} = 4 × 10^{14}

3 × 10^{17} = 3 × 10^{3} × 10^{14}

= 3 × 1000 × 10^{14} = 3000 × 10^{4}

∴ 3000 × 10^{14} > 4 × 10^{4}

∴ 4 × 10^{14} > 3 × 10^{17}