Question

$\frac{(243{)}^{n/5}\times 3^{2n+1}}{9^n\times 3^{n-1}}=?$

Answer 1

Given Expression = $\frac{(243{)}^{\left(n/5\right)}\times 3^{2n+1}}{9^n\times 3^{n-1}}$
$=\frac{(3^5{)}^{\left(n/5\right)}\times 3^{2n+1}}{(3^2{)}^n\times 3^{n-1}}$
$=\frac{(3^{5^{(}n/5)}\times 3^{2n+1})}{(3^{2n}\times 3^{n-1})}$
$=\frac{3^n\times 3^{2n+1}}{3^{2n}\times 3^{2n-1}}$
$=\frac{3^{(n+2n+1)}}{3^{(2n+n-1)}}$
$=\frac{3^{3n+1}}{3^{3n-1}}$
$=3^{(3n+1-3n+1)}=3^2=9.$