Quantitative Aptitude Ques 1496

Question: The value of $ {{(125)}^{\frac{4}{3}}}\div {{(5)}^{3}}\times {{( \frac{1}{8} )}^{\frac{4}{3}}}\times {{(\sqrt{3})}^{4}} $

Options:

A) (a) $ 12 $

B) $ \frac{44}{39} $

C) $ 16 $

D) $ \frac{45}{8} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ {{(125)}^{4/3}}\div {{(5)}^{3}}\times {{( \frac{1}{8} )}^{4/3}}\times {{(\sqrt{3})}^{4}} $ $ ={{(5^{3})}^{4/3}}\div {{(5)}^{3}}\times {{( \frac{1}{2} )}^{3\times \frac{4}{3}}}\times {{(\sqrt{3})}^{4}} $ $ ={{(5)}^{4}}\times \frac{1}{{{(5)}^{3}}}\times {{( \frac{1}{2} )}^{4}}\times {{(\sqrt{3})}^{4}} $ $ =625\times \frac{1}{125}\times \frac{1}{8}\times 9=5\times \frac{1}{8}\times 9=\frac{45}{8} $
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