Quantitative Aptitude Ques 1151

Question: The value of $ \frac{{{(8.1)}^{3.6}}\times {{(9)}^{2.7}}}{{{(81)}^{4.2}}\times (3)} $ is

Options:

A) 3

B) 6

C) 9

D) 8.2

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ \frac{{{(81)}^{3.6}}\times {{(9)}^{2.7}}}{{{(81)}^{4.2}}\times 3}=\frac{{{(3^{4})}^{3.6}}\times {{(3^{2})}^{2.7}}}{{{(3^{4})}^{4.2}}\times 3} $ $ =\frac{{3^{14.4}}\times {3^{5.4}}}{{3^{16.6}}\times 3^{1}}={3^{14.4+5.4-16.8-1}} $ $ [ \begin{aligned} & \because a^{m}\times a^{n}={{(a)}^{m+n}} \\ & a^{m}\div a^{n}={{(a)}^{m-n}} \\ \end{aligned} ] $ $ ={3^{19.8-17.8}}=3^{2}=9 $
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