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

Explanation: According to laws of exponents, a

^{m/n}= \((\sqrt[n]{a})^m\).

Applying that rule here, 8

^{2/3}= \((\sqrt[3]{8})^2\)

= 2

^{2}

= 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

Explanation: According to laws of exponents, a

^{m/n}= \((\sqrt[n]{a})^m\).

Applying that rule here, 3

^{3/2}= (3

^{3})

^{1/2}

= 27

^{1/2}

= \(\sqrt{27}\).

3. By simplifying (5)^{3/8}, we get __________

a) (5)^{3}/(5^{8})

b) (125)^{1/8}

c) (5)^{8}/(5)^{3}

d) 5^{24}

View Answer

Explanation: According to laws of exponents, a

^{m/n}= \((\sqrt[n]{a})^m\).

Applying that rule here, 5

^{3/8}= (5

^{3})

^{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

View Answer

Explanation: According to laws of exponents, a

^{m}a

^{n}= 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}

= 3

^{1}= 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

Explanation: According to laws of exponents, a

^{m}a

^{n}= 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

View Answer

Explanation: According to laws of exponents, a

^{m}a

^{n}= 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

Explanation: According to laws of exponents, a

^{m}/a

^{n}= 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) 4^{27}

b) 4^{6}

c) 4^{12}

d) 4^{3}

View Answer

Explanation: According to laws of exponents, a

^{m}/a

^{n}= a

^{m-n}

Applying that rule here, (4)

^{9}/(4)

^{3}= 4

^{(9-3)}

= 4

^{6}.

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

Explanation: According to laws of exponents, a

^{m}/a

^{n}= 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) 64^{3}

d) 16

View Answer

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 2^{3}*5^{3}, we get __________

a) 10^{6}

b) 100

c) 1000

d) 10^{9}

View Answer

Explanation: According to laws of exponents, (a

^{m})*(b

^{m}) = (ab)

^{m}

Applying that rule here, 2

^{3}*5

^{3}=(2*5)

^{3}

=(10)

^{3}

= 1000.

12. By simplifying (2)^{1/2}/(18)^{-1/2}, we get __________

a) 36

b) 36^{2}

c) 9

d) 6

View Answer

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.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

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