The value of $$\frac{{{{\left( {243} \right)}^{\frac{n}{5}}}{{.3}^{2n + 1}}}}{{{9^n}{{.3}^{n - 1}}}}{\text{ is?}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{{{\left( {243} \right)}^{\frac{n}{5}}}{{.3}^{2n + 1}}}}{{{9^n}{{.3}^{n - 1}}}} \cr & = \frac{{{{\left( {{3^5}} \right)}^{\frac{n}{5}}}{{.3}^{2n + 1}}}}{{{3^{2n}}{{.3}^{n - 1}}}} \cr & = \frac{{{3^{n + 2n + 1}}}}{{{3^{2n + n - 1}}}} \cr & = \frac{{{3^{3n + 1}}}}{{{3^{3n - 1}}}} \cr & = {3^{3n + 1 - 3n + 1}} \cr & = {3^2} \cr & = 9 \cr} $$