Aptitude Question ID : 93824

Find out the value of
\frac{(243)^{\frac{n}{5}}.3^{2n+1}}{9^{n}.3^{n-1}}
[A]1
[B]3^{n}
[C]9
[D]3

9
Given Expression,
= \frac{(243)^{\frac{n}{5}}.3^{2n+1}}{9^{n}.3^{n-1}}
=> \frac{(3^{5})^{\frac{n}{5}}\times 3^{2n+1}}{(3^{2})^{n}\times 3^{n-1}} = \frac{3^{n}\times 3^{2n+1}}{3^{2n}\times 3^{n-1}}
=> \frac{3^{n+2n+1}}{3^{2n+n-1}} = \frac{3^{3n+1}}{3^{3n-1}}
=> 3^{3n+1-3n+1} = 3^{2} = 9
Hence option [C] is the right answer.

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