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

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

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New post 17 Dec 2018, 23:19
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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Concentration: Sustainability, Marketing
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Re: What is the value of 44^(5/2)/(11^(3/2))?  [#permalink]

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New post 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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New post 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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