# 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

Explanation: According to laws of exponents, am/n = $$(\sqrt[n]{a})^m$$.
Applying that rule here, 82/3 = $$(\sqrt{8})^2$$
= 22
= 4.

2. By simplifying (3)3/2, we get __________
a) (3)3/(3)2
b) (3)2/(3)3
c) $$\sqrt{27}$$
d) $$\sqrt{9}$$

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

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.

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

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

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.

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

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) $$\sqrt{5}$$
d) $$\sqrt{5}$$

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
= $$\sqrt{5}$$.

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

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) $$\frac{1}{\sqrt{13}}$$
d) $$\frac{1}{\sqrt{13}}$$

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.

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

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

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

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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