[CLASS 8] Mathematics MCQs on Laws of Exponents and Answers

Mathematics Multiple Choice Questions & Answers on “Laws of Exponents”.

1. Find the value of (frac{1}{8^{-2}}).
a) (frac{1}{16})
b) (frac{1}{64})
c) 16
d) 64

Answer: d
Clarification: (frac{1}{a^{-m}}) = a^m
⇒ (frac{1}{8^{-2}}) = 8² = 64.

2. What is 2^-3?
a) (frac{1}{4})
b) (frac{1}{8})
c) 4
d) 8

Answer: b
Clarification: a^-m = (frac{1}{a^m})
⇒ 2^-3 = (frac{1}{2^3}) = (frac{1}{8}).

3. Find the value of 16^-2 × 16¹⁴.
a) 16¹²
b) 16^-12
c) 16¹⁴
d) 16^-14

Answer: a
Clarification: a^m × aⁿ = a^{m + n}
⇒ 16^-2 × 16¹⁴ = 16^{-2 + 14} = 16¹².

4. Evaluate ((frac{21^{29}}{21^5})).
a) 21²⁵
b) 21^-25
c) 21²⁴
d) 21^-24

Answer: c
Clarification: (frac{a^m}{a^n}) = a^{m – n}
⇒ ((frac{21^{29}}{21^5})) = 21^{29 – 5} = 21²⁴.

5. Match the pairs.

a) 1-b, 2-c, 3-d
b)1-b, 2-c, 3-a
c) 1-c, 2-b, 3-a
d) 1-c, 2-b, 3-d

Answer: b
Clarification: a^m × b^m = (ab)^m
⇒ 2³ × 8³ = (2 × 8)³ = 16³
Now, (frac{a^m}{b^m} = (frac{a}{b})^m)
⇒ ((frac{8}{2})^3) = 4³
Also, (a^m)ⁿ = a^mn, a⁰ = 1
⇒ (2³)⁰ = 2^{3 × 0} = 2⁰ = 1.

6. Find the value of (2³)².
a) 128
b) 16
c) 32
d) 64

Answer: d
Clarification: (a^m)ⁿ = a^mn
⇒ (2³)² = 2⁶ = 64.