The value of ( 243 )^n/5.3^2n + 19^n.3^n - 1 is?

Answer: Option B

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