## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1

- Class 7 Maths Exponents and Powers Exercise 13.1
- Class 7 Maths Exponents and Powers Exercise 13.2
- Class 7 Maths Exponents and Powers Exercise 13.3

**NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.1**

Question 1.

Find the value of

(i) 2^{6}

(ii) 9^{3}

(iii) 11^{2}

(iv) 5^{4}

Solution:

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

(ii) 9^{3} = 9 × 9 × 9 = 729

(iii) 11^{2} = 11 × 11 = 121

(iv) 5^{4} = 5 × 5 × 5 × 5 = 625

Question 2.

Exress 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 = 6^{3}

(ii) t × t = t^{2}

(iii) b × b × b × b = b^{4}

(iv) 5 × 5× 7 × 7 × 7 = 5^{2} × 7^{3} = 5^{2} · 7^{3}

(v) 2 × 2 × a × a = 2^{2} × a^{2} = 2^{2} · a^{2}

(vi) a × a ×a × c × c × c × c × d = a^{3} × c^{4} × d = a^{3} · c^{4} · d

Question 3.

Express each of the following numbers using exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Solution:

Question 4.

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

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

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

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

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

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

Solution:

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

4^{3} = 4 × 4 × 4 = 64,

3^{4} = 3 × 3 × 3 × 3 = 81

Since 81 > 64

∴ 34 is greater than 43.

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

5^{3} = 5 × 5 × 5 = 125

3^{5} = 3 × 3 × 3 × 3 × 3 = 243

Since 243 > 125

∴ 35 is greater than 53.

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

2^{8} =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8^{2} = 8 × 8 = 64

Since 256 > 64

∴ 28 is greater than 28.

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

100^{2} = 100 × 100 = 10000

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

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

10^{2} = 10 × 10 = 100

Since 1024 > 100

∴ 210 is greater than 102.

Question 5.

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

(i) 648

(ii) 405

(iii) 540

(iv) 3600

Solution:

Question 6.

Simplify:

(i) 2 × 10^{3}

(ii) 7^{2} × 2^{2}

(iii) 2^{3} × 5

(iv) 3 × 4^{4}

(v) 0 × 10^{2}

(vi) 5^{2} × 3^{3}

(vii) 2^{4} × 3^{2}

(viii) 3^{2} × 10^{4}

Solution:

(i) 2 × 10^{3} = 2 × 10 × 10 × 10 = = 2000

(ii) 7^{2} × 2^{2} = = 7 × 7 × 2 × 2 = 196

(iii) 2^{3} × 5 = 2 × 2 × 2 × 5 = 40

(iv) 3 × 4^{4} = 3 × 4 × 4 × 4 × 4 = 768

(v) 0 × 10^{2} = 0 × 10 × 10 = = 0

(vi) 5^{2} × 3^{3} = 5 × 5 × 3 × 3 × 3 = 675

(vii) 2^{4} × 3^{2} = 2 × 2 × 2 × 2 × 3 × 3 = 144

(viii) 3^{2} × 10^{4} = 3 × 3 × 10 × 10 × 10 × 10 = 90000

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}

= 15^{2} = 225 [∵ a^{m} × b^{m} = (ab)^{m})

(iv) (-2)^{3} × (-10)^{3} = [(-2) × (-10)]^{3}

= 20^{2} = 8000 [∵ a^{m} × b^{m} = (ab)^{m}]

Question 8.

Compare the following:

(i) 2.7 × 10^{12}; 1.5 × 10^{8}

(ii) 4 × 10^{14}; 3 × 10^{14}

Solution:

(i) 2.7 × 10^{12}; 1.5 × 10^{8}

Here, 10^{12} > 10^{8}

∴ 2.7 × 10^{12}> 1.5 × 10^{8}

(ii) 4 × 10^{14}; 3 × 10^{17}

Here, 10^{17} > 10^{14}

∴ 4 × 10^{14} < 3 × 10^{17}

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