Real Numbers Exponents Laws Questions and Answers

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Laws of Exponents for Real Numbers”.

1. By simplifying (8)^2/3, we get __________
a) 4
b) 16
c) (8)²/(8)³
d) 32
View Answer

Answer: a
Explanation: According to laws of exponents, a^m/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 8^2/3 = \((\sqrt[3]{8})^2\)
= 2²
= 4.

2. By simplifying (3)^3/2, we get __________
a) (3)³/(3)²
b) (3)²/(3)³
c) \(\sqrt{27}\)
d) \(\sqrt[3]{9}\)
View Answer

Answer: c
Explanation: According to laws of exponents, a^m/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 3^3/2 = (3³)^1/2
= 27^1/2
= \(\sqrt{27}\).

3. By simplifying (5)^3/8, we get __________
a) (5)³/(5⁸)
b) (125)^1/8
c) (5)⁸/(5)³
d) 5²⁴
View Answer

Answer: b
Explanation: According to laws of exponents, a^m/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 5^3/8= (5³)^1/8
= (5*5*5)^1/8
= (125)^1/8.

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4. By simplifying (3)^1/3 * (3)^2/3, we get __________
a) (3)^2/9
b) (3)^-1/9
c) 9
d) 3
View Answer

Answer: d
Explanation: According to laws of exponents, a^m aⁿ = a^(m+n)
Applying that rule here, (3)^1/3 * (3)^2/3 = 3^(1/3+2/3)
= 3^(1+2)/3
= 3^3/3
= 3¹ = 3.

5. By simplifying (7)^2/5 * (7)^3/4, we get __________
a) (7)^6/20
b) 7
c) (7)^23/20
d) (7)^-7/20
View Answer

Answer: c
Explanation: According to laws of exponents, a^m aⁿ = a^(m+n)
Applying that rule here, (7)^2/5 * (7)^3/4 = (7)^(2/5+3/4)
= (7)^{((2*4)+(5*3))/(5*4)}
= (7)^(8+15)/20
= (7)^23/20.

Check this: Class 9 - Mathematics Books | Class 10 Mathematics MCQs

6. By simplifying (9)^1/4 * (9)^7/4, we get __________
a) 81
b) 9
c) 3
d) 27
View Answer

Answer: a
Explanation: According to laws of exponents, a^m aⁿ = a^(m+n)
Applying that rule here, (9)^1/4 * (9)^7/4 = (9)^(1+7)/4
= (9)^8/4
= (9)²
= 81.

7. By simplifying (5)^3/4/(5)^1/4, we get __________
a) (5)^1/4
b) (5)^3/16
c) \(\sqrt[3]{5}\)
d) \(\sqrt[2]{5}\)
View Answer

Answer: d
Explanation: According to laws of exponents, a^m/aⁿ = a^m-n
Applying that rule here, (5)^3/4/(5)^1/4 = (5)^(3/4-1/4)
= (5)^(3-1)/4
= (5)^2/4
= (5)^1/2
= \(\sqrt[2]{5}\).

8. By simplifying (4)⁹/(4)³, we get __________
a) 4²⁷
b) 4⁶
c) 4¹²
d) 4³
View Answer

Answer: b
Explanation: According to laws of exponents, a^m/aⁿ = a^m-n
Applying that rule here, (4)⁹/(4)³ = 4^(9-3)
= 4⁶.

9. By simplifying (13)^1/2/(13)^7/2, we get __________
a) 13^7/4
b) 13^-3
c) \(\frac{1}{\sqrt[2]{13}}\)
d) \(\frac{1}{\sqrt[3]{13}}\)
View Answer

Answer: b
Explanation: According to laws of exponents, a^m/aⁿ = a^m-n
Applying that rule here, (13)^1/2/(13)^7/2 = 13^(1/2-7/2)
= 13^{((1)-(7))/(2)}
= 13^((-6))/(2)
= 13^-3.

10. By simplifying (4)^1/3*(16)^1/3, we get __________
a) 4
b) 8
c) 64³
d) 16
View Answer

Answer: a
Explanation: According to laws of exponents, (a^m)*(b^m) = (ab)^m
Applying that rule here, (4)^1/3*(16)^1/3 = (4*16)^1/3
= (64)^1/3
= 4.

11. By simplifying 2³*5³, we get __________
a) 10⁶
b) 100
c) 1000
d) 10⁹
View Answer

Answer: c
Explanation: According to laws of exponents, (a^m)*(b^m) = (ab)^m
Applying that rule here, 2³*5³=(2*5)³
=(10)³
= 1000.

12. By simplifying (2)^1/2/(18)^-1/2, we get __________
a) 36
b) 36²
c) 9
d) 6
View Answer

Answer: d
Explanation: We know that according to laws of exponents, 1/18^-1/2 = 18^1/2
Hence, (2)^1/2/(18)^-1/2 =(2)^1/2 (18)^1/2
According to laws of exponents, (a^m)*(b^m) = (ab)^m
Applying that rule here, (2)^1/2 (18)^1/2 = (2*18)^1/2
= (36)^1/2
= 6.

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