Exponents and Powers Class 8 Extra Questions with Answers

These Class 8 Maths Extra Questions Chapter 12 Exponents and Powers will help students prepare well for the exams.

Class 8 Maths Chapter 12 Extra Questions Exponents and Powers

Class 8 Maths Exponents and Powers Extra Questions

Question 1.
Express the number 1496000000000 in standard form.
Solution:
1496000000000 = 1496 × 10⁹ (or) 1.496 × 10¹²

Question 2.
What should 69^-3 be multiplied by to get 1 ? Show your steps.
Solution:

Question 3.
What would you put in the place of ’?’ to balance the equation ?
6.807 × 10⁶ × ? = 6.807 × 10¹⁰
Solution:
6.807 × 10⁶ × ? = 6.807 × 10¹⁰[∵ a^{m + n} = a^m × aⁿ]
6.807 × 10⁶ × ? = 6.807 × 10⁶ × 10⁴
? = 10⁴

Exponents and Powers Extra Questions Class 8

Question 1.
Find the value of 256^0.16 × 16^0.18.
Solution:
256^0.16 × 16^0.18

= (2⁸)^0.16 × (2⁴)^0.18 [∵ (a^m)ⁿ = a^{m × n}]
= 2^1.28 × 2^0.72
[∵ a^m × aⁿ = a^{m + n}]
= 2^{1.28 × 0.72}
= 2²
= 4

Question 2.
Find the value of ’n’ in the following equation: \(\frac{7^{2 n+1}}{49}\) = 7³
Solution:
\(\frac{7^{2 n+1}}{49}\) = 7³
\(\frac{7^{2 n+1}}{7^2}\) = 7³
7^{2n + 1 – 2} = 7³ [∴ \(\frac{a^m}{a^n}\) = a^{m – n}]
7^{2n – 1} = 7³
∴ 2n – 1 = 3 [∵ If a^m = aⁿ then m = n]
2n = 3 + 1
2n = 4
n = \(\frac{4}{2}\) = 2
n = 2

Exponents and Powers Class 8 Extra Questions

Question 1.
Find the value of
i) 2^-3
ii) \(\frac{1}{3^{-2}}\)
Solution:
i) 2^-3 = \(\frac{1}{2^{3}}\) = \(\frac{1}{8}\)
ii) \(\frac{1}{3^{-2}}\) = 3² = 3 × 3 = 9

Question 2.
Simplify
i) (- 4)⁵ × (- 4)^-10
ii) 2⁵ ÷ 2^-6
Solution:
i) (- 4)⁵ × (- 4)^-10 = (- 4)^{5 -10} = (- 4)^-5 = \(\frac{1}{(-4)^5}\) (a^m × aⁿ = ^{m + n}, a^-m = \(\frac{1}{a^{\mathrm{m}}}\))
ii) 2⁵ ÷ 2^-6 = 2^{5 – (- 6)} = 2¹¹ (a^m ÷ aⁿ = a^{m – n})

Question 3.
Express 4^-3 as a power with the base 2.
Solution:
We have, 4 = 2 × 2 = 2²
Therefore, (4)^-3 = (2 × 2)^-3 = (2²)^-3 = 2^{2 × (-3)} = 2^-6 [(a^m)ⁿ = a^mn]

Question 4.
Simplify and write the answer in the exponential form.
i) (2⁵ ÷ 2⁸)⁵ × 2^-5
ii) (-4)^-3 × (5)^-3 × (-5)^-3
iii) \(\frac{1}{8}\) × (3)^-3
iv) (- 3)⁴ × (\(\frac{5}{3}\))⁴
Solution:
i) (2⁵ ÷ 2⁸)⁵ × 2^-5 = (2^{5 – 8})⁵ × 2^-5 = (2^-3)⁵ × 2^-5 = 2^{– 15 – 5} = 2^-20 = \(\frac{1}{2^{20}}\)

ii) (-4)^-3 × (5)^-3 × (-5)^-3 = [(- 4) × 5 × (-5)]^-3 = [100]^-3 = \(\frac{1}{100^{3}}\)
[using the law a^m bⁿ = (ab)^m, a^-m = \(\frac{1}{a^m}\)]

iii) \(\frac{1}{8}\) × (3)^-3 = \(\frac{1}{2^{3}}\) × (3)^-3 = 2^-3 × 3^-3 = (2 × 3)^-3 = 6^-3 = \(\frac{1}{6^{3}}\)

iv) (-3)⁴ × (\(\frac{5}{3}\))⁴ = (-1 × 3 )⁴ × \(\frac{5^4}{3^4}\) = (-1)⁴ × 3⁴ × \(\frac{5^4}{3^4}\)
= (-1)⁴ × 5⁴ = 5⁴ [(-1)⁴ = 1]

Question 5.
Find m so that (- 3)^{m + n} × (-3)⁵ = (-3)⁷
Solution:
(-3)^{m + n} × (-3)⁵ = (-3)⁷
(-3)^{m + 1 + 5} = (-3)⁷
(-3)^{m + 6} = (-3)⁷
On both the sides powers have the same base different from 1 and -1, so their exponents must be equal.
Therefore, m + 6 = 7
or m = 7 – 6 = 1

Question 6.
Find the value of (\(\frac{2}{3}\))^-2
Solution:
(\(\frac{2}{3}\))^-2 = \(\frac{2^{-2}}{3^{-2}}\) = \(\frac{3^2}{2^2}\) = \(\frac{9}{4}\)

Question 7.
Simplify i) {(\(\frac{1}{3}\))^-2 – (\(\frac{1}{2}\))^-3} (\(\frac{1}{4}\))^-2
ii) (\(\frac{5}{8}\))^-7 × (\(\frac{8}{5}\))^-5
Solution:

Question 8.
Express the following numbers in standard form.
i) 0.000035
ii) 4050000
Solution:
i) 0.000035 = 3.5 × 10^-5
ii) 4050000 = 4.05 × 10⁶

Question 9.
Express the following numbers in usual form.
i) 3.52 × 10⁵
ii) 7.54 × 10^-4
iii) 3 × 10^-5
Solution:
i) 3.52 × 10⁵ = 3.52 × 100000 = 352000

ii) 7.54 × 10^-4 = \(\frac{7.54}{10^4}\) = \(\frac{7.54}{10000}\) = 0.000754

iii) 3 × 10⁵ = \(\frac{3}{10^5}\) = \(\frac{3}{100000}\) = 0.00003