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

Answer:

Explanation:

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