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# What is the value of 44^(5/2)/(11^(3/2))?

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Math Expert
Joined: 02 Sep 2009
Posts: 52113
What is the value of 44^(5/2)/(11^(3/2))?  [#permalink]

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17 Dec 2018, 23:19
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:22) correct 24% (01:48) wrong based on 46 sessions

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What is the value of $$\frac{44^{\frac{5}{2}}}{\sqrt{11^3}}$$ ?

A. 11
B. 32
C. 176
D. 352
E. 704

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Joined: 18 Aug 2017
Posts: 1150
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: What is the value of 44^(5/2)/(11^(3/2))?  [#permalink]

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18 Dec 2018, 03:41
Bunuel wrote:
What is the value of $$\frac{44^{\frac{5}{2}}}{\sqrt{11^3}}$$ ?

A. 11
B. 32
C. 176
D. 352
E. 704

expression can be written as :

44*44* sqrt 11 * 2/ 11 sqrt 11

solve we would get 352 IMO D
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What is the value of 44^(5/2)/(11^(3/2))?  [#permalink]

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18 Dec 2018, 19:30
1
Bunuel wrote:
What is the value of $$\frac{44^{\frac{5}{2}}}{\sqrt{11^3}}$$ ?

A. 11
B. 32
C. 176
D. 352
E. 704

Simplifying the numerator of the given expression:-

$$44^{\frac{5}{2}}$$=$$(11*4)^{\frac{5}{2}}$$=$$11^{\frac{5}{2}}*4^{\frac{5}{2}}$$

Simplifying the denominator of the given expression:-
$${\sqrt{11^3}}$$=$$11^{\frac{3}{2}}$$

Now, $$\frac{numerator}{denominator}=11^{\frac{5}{2}-\frac{3}{2}}*4^{\frac{5}{2}}$$=$$11*2^5$$=352

Ans. (D)

Properties of exponents used:-
1) $$\frac{a^m}{a^n}=a^{m-n}$$
2) $$(a^m)^n=a^{m*n}$$
3) $$(a*b)^m=a^m*b^m$$
4) $$\sqrt{a^m}=a^{\frac{m}{2}}$$
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What is the value of 44^(5/2)/(11^(3/2))? &nbs [#permalink] 18 Dec 2018, 19:30
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