Quantitative Aptitude Ques 2154

Question: The value of $ \frac{(243)\times (243)}{(7)\times (49)\times (343)} $ is

Options:

A) $ \frac{3}{7} $

B) $ \frac{7}{3} $

C) $ 1\frac{3}{7} $

D) $ 2\frac{2}{7} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \frac{{{(243)}^{0.13}}\times {{(243)}^{0.07}}}{{7^{0.25}}\times {{(49)}^{0.075}}\times {{(343)}^{0.2}}}=\frac{{{(243)}^{(0.13+0.07)}}}{{7^{0.25}}\times {{(7^{2})}^{(0.075)}}\times {{(7^{3})}^{0.2}}} $ $ =\frac{{{(243)}^{0.2}}}{{7^{0.25}}\times {{(7)}^{2\times ,}}^{0.075}\times {{(7)}^{3\times ,}}^{0.2}} $ $ =\frac{{{(3^{5})}^{0.2}}}{{7^{0.25}}\times {7^{0.15}}\times {7^{0.60}}} $ $ =\frac{{5^{(5,\times ,0.2)}}}{{7^{(0.25,+,0.15,+,0.6)}}}=\frac{3^{1}}{7^{1}}=\frac{3}{7} $
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