( 243 )^n/5 × 3^2n + 19^n × 3^n - 1 = ?

Answer: Option C

$$\begin{array}{rl}& \text{Given}\text{Expression}\\ & =\frac{{\left(243\right)}^{n/5}\times 3^{2n+1}}{9^n\times 3^{n-1}}\\ & =\frac{{\left(3^5\right)}^{n/5}\times 3^{2n+1}}{{\left(3^2\right)}^n\times 3^{n-1}}\\ & =\frac{\left(3^{5\times \left(n/5\right)}\times 3^{2n+1}\right)}{\left(3^{2n}\times 3^{n-1}\right)}\\ & =\frac{3^n\times 3^{2n+1}}{3^{2n}\times 3^{n-1}}\\ & =\frac{3^{\left(n+2n+1\right)}}{3^{\left(2n+n-1\right)}}\\ & =\frac{3^{3n+1}}{3^{3n-1}}\\ & =3^{\left(3n+1-3n+1\right)}\\ & =3^2\\ & =9\end{array}$$