\(\frac{(243)^{n/5}\times 3^{2n+1}}{9^{n}\times 3^{n-1}}=?\)
Answer: C
Given Expression = \(\frac{(243)^{(n/5)}\times 3^{2n+1}}{9^{n}\times 3^{n-1}}\)
\(=\frac{(3^{5})^{(n/5)}\times 3^{2n+1}}{(3^{2})^{n}\times 3^{n-1}}\)
\(=\frac{(3^{5\times(n/5))}\times 3^{2n+1}}{(3^{2n}\times 3^{n-1})}\)
\(=\frac{3^{n\times3^{2n+1}}}{3^{2n}\times3^{n-1}}\)
\(=\frac{3^{(n+2n+1)}}{3^{(2n+n-1)}}\)
\(=\frac{3^{3n+1}}{3^{3n-1}}\)
\(=3^{(3n+1-3n+1)}=3^{2}=9\)