Mathematics Questions and Answers – Laws of Exponents for Real Numbers

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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, am/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 82/3 = \((\sqrt[3]{8})^2\)
= 22
= 4.
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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, am/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 33/2 = (33)1/2
= 271/2
= \(\sqrt{27}\).

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, am/n = \((\sqrt[n]{a})^m\).
Applying that rule here, 53/8= (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, am an = a(m+n)
Applying that rule here, (3)1/3 * (3)2/3 = 3(1/3+2/3)
= 3(1+2)/3
= 33/3
= 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, am 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.
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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, am 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, am/an = am-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
= \(\sqrt[2]{5}\).
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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, am/an = am-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) 137/4
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, am/an = am-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.
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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, (am)*(bm) = (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, (am)*(bm) = (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 = 181/2
Hence, (2)1/2/(18)-1/2 =(2)1/2 (18)1/2
According to laws of exponents, (am)*(bm) = (ab)m
Applying that rule here, (2)1/2 (18)1/2 = (2*18)1/2
= (36)1/2
= 6.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter