# Mathematics Questions and Answers – Laws of Exponents

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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

Explanation: $$\frac{1}{a^{-m}}$$ = am
⇒ $$\frac{1}{8^{-2}}$$ = 82 = 64.

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

Explanation: 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

Explanation: am × an = am + n
⇒ 16-2 × 1614 = 16-2 + 14 = 1612.
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4. Evaluate $$(\frac{21^{29}}{21^5})$$.
a) 2125
b) 21-25
c) 2124
d) 21-24

Explanation: $$\frac{a^m}{a^n}$$ = am – n
⇒ $$(\frac{21^{29}}{21^5})$$ = 2129 – 5 = 2124.

5. Match the pairs.

 A B 1) 23 × 83 a. 1 2) $$\frac{8^3}{2^3}$$ b. 163 3) (23)0 c. 43 d. 8

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

Explanation: am × bm = (ab)m
⇒ 23 × 83 = (2 × 8)3 = 163
Now, $$\frac{a^m}{b^m} = (\frac{a}{b})^m$$
⇒ ($$\frac{8}{2})^3$$ = 43
Also, (am)n = amn, a0 = 1
⇒ (23)0 = 23 × 0 = 20 = 1.

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

Explanation: (am)n = amn
⇒ (23)2 = 26 = 64.

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