# Exponents and Powers Class 7 Extra Questions Maths Chapter 13

**Extra Questions for Class 7 Maths Chapter 13 Exponents and Powers**

### Exponents and Powers Class 7 Extra Questions Very Short Answer Type

Question 1.

Express 343 as a power of 7.

Solution:

We have 343 = 7 × 7 × 7 = 7^{3}

Thus, 343 = 7^{3}

Question 2.

Which is greater 3^{2} or 2^{3}?

Solution:

We have 3^{2} = 3 × 3 = 9

2^{3} = 2 × 2 × 2 = 8

Since 9 > 8

Thus, 3^{2} > 2^{3}

Question 3.

Express the following number as a powers of prime factors:

(i) 144

(ii) 225

Solution:

(i) We have

144 = 2 × 2 × 2 × 2 × 3 × 3 = 2^{4} × 3^{2}

Thus, 144 = 2^{4} × 3^{2}

(ii) We have

225 = 3 × 3 × 5 × 5 = 3^{2} × 5^{2}

Thus, 225 = 3^{2} × 5^{2}

Question 4.

Find the value of:

(i) (-1)^{1000}

(ii) (1)^{250}

(iii) (-1)^{121}

(iv) (10000)^{0}

Solution:

(i) (-1)^{1000} = 1 [∵ (-1)^{even number} = 1]

(ii) (1)^{250} = 1 [∵ (1)^{even number} = 1]

(iii) (-1)^{121} = -1 [∵ (-1)^{odd number} = -1]

(iv) (10000)^{0} = 1 [∵ a^{0} = 1]

Question 5.

Express the following in exponential form:

(i) 5 × 5 × 5 × 5 × 5

(ii) 4 × 4 × 4 × 5 × 5 × 5

(iii) (-1) × (-1) × (-1) × (-1) × (-1)

(iv) a × a × a × b × c × c × c × d × d

Solution:

(i) 5 × 5 × 5 × 5 × 5 = (5)^{5}

(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4^{3} × 5^{3}

(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)^{5}

(iv) a × a × a × b × c × c × c × d × d = a^{3}b^{1}c^{3}d^{2}

Question 6.

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

(i) 405

(ii) 504

(iii) 500

Solution:

(i) We have

405 = 3 × 3 × 3 × 3 × 5 = 3^{4} × 5^{1}

Thus, 405 = 3^{4} × 5^{1}

(ii) We have

504 = 2 × 2 × 2 × 3 × 3 × 7 = 2^{3} × 3^{2} × 7^{1}

Thus, 504 = 2^{3} × 3^{2} × 7^{1}

(iii) We have

500 = 2 × 2 × 5 × 5 × 5 = 2^{2} × 5^{3}

Thus, 500 = 2^{2} × 5^{3}

Question 7.

Simplify the following and write in exponential form:

(i) (5^{2})^{3}

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

(iii) (a^{b})^{c}

(iv) [(5)^{2}]^{2}

Solution:

(i) (5^{2})^{3} = 5^{2×3} = 5^{6}

(ii) (2^{3})^{3} = 2^{3×3} = 2^{9}

(iii) (a^{b})^{c} = a^{b×c} = a^{bc}

(iv) [(5)^{2}]^{2} = 5^{2×2} = 5^{4}

Question 8.

Verify the following:

Solution:

Question 9.

Simplify:

Solution:

Question 10.

Simplify and write in exponential form:

Solution:

### Exponents and Powers Class 7 Extra Questions Short Answer Type

Question 11.

Express each of the following as a product of prime factors is the exponential form:

(i) 729 × 125

(ii) 384 × 147

Solution:

(i) 729 × 125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 = 3^{6} × 5^{3}

Thus, 729 × 125 = 3^{6} × 5^{3}

(ii) 384 × 147 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7 = 2^{7} × 3^{2} × 7^{2}

Thus, 384 × 147 = 2^{7} × 3^{2} × 7^{2}

Question 12.

Simplify the following:

(i) 10^{3} × 9^{0} + 3^{3} × 2 + 7^{0}

(ii) 6^{3} × 7^{0} + (-3)^{4} – 9^{0}

Solution:

(i) 10^{3} × 9^{0} + 3^{3} × 2 + 7^{0}

= 1000 + 54 + 1

= 1055

(ii) 6^{3} × 7^{0} + (-3)^{4} – 9^{0}

= 216 × 1 + 81 – 1

= 216 + 80

= 296

Question 13.

Write the following in expanded form:

(i) 70,824

(ii) 1,69,835

Solution:

(i) 70,824

= 7 × 10000 + 0 × 1000 + 8 × 100 + 2 × 10 + 4 × 10^{0}

= 7 × 10^{4} + 8 × 10^{2} + 2 × 10^{1} + 4 × 10^{0}

(ii) 1,69,835

= 1 × 100000 + 6 × 10000 + 9 × 1000 + 8 × 100 + 3 × 10 + 5 × 10^{0}

= 1 × 10^{5} + 6 × 10^{4} + 9 × 10^{3} + 8 × 10^{2} + 3 × 10^{1} + 5 × 10^{0}

Question 14.

Find the number from each of the expanded form:

(i) 7 × 10^{8} + 3 × 10^{5} + 7 × 10^{2} + 6 × 10^{1} + 9

(ii) 4 × 10^{7} + 6 × 10^{3} + 5

Solution:

(i) 7 × 10^{8} + 3 × 10^{5} + 7 × 10^{2} + 6 × 10^{1} + 9

= 7 × 100000000 + 3 × 100000 + 7 × 100 + 6 × 10 + 9

= 700000000 + 300000 + 700 + 60 + 9

= 700300769

(ii) 4 × 10^{7} + 6 × 10^{3} + 5

= 4 × 10000000 + 6 × 1000 + 5

= 40000000 + 6000 + 5

= 40006005

Question 15.

Find the value of k in each of the following:

Solution:

Question 16.

Find the value of

(a) 3^{0} ÷ 4^{0}

(b) (8^{0} – 2^{0}) ÷ (8^{0} + 2^{0})

(c) (2^{0} + 3^{0} + 4^{0}) – (4^{0} – 3^{0} – 2^{0})

Solution:

(a) We have 3^{0} ÷ 4^{0} = 1 ÷ 1 = 1 [∵ a^{0} = 1]

(6) (8^{0} – 2^{0}) ÷ (8^{0} + 2^{0}) = (1 – 1) ÷ (1 + 1) = 0 ÷ 2 = 0

(c) (2^{0} + 3^{0} + 4^{0}) – (4^{0} – 3^{0} – 2^{0})

= (1 + 1 + 1) – (1 – 1 – 1) [∵ a^{0} = 1]

= 3 – 1

= 2

Question 17.

Express the following in standard form:

(i) 8,19,00,000

(ii) 5,94,00,00,00,000

(iii) 6892.25

Solution:

(i) 8,19,00,000 = 8.19 × 10^{7}

(ii) 5,94,00,00,00,000 = 5.94 × 10^{11}

(iii) 6892.25 = 6.89225 × 10^{3}

Question 18.

Evaluate:

Solution:

### Exponents and Powers Class 7 Extra Questions Higher Order Thinking Skills (HOTS) Type

Question 19.

Find the value of x, if

Solution:

Question 20.

Solution: