Question

Find the value of $\frac{(243{)}^{\frac{n}{5}}\times 3^{2n+1}}{9^n\times 3^{n-1}}$

Answer 1

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

$3^2=9$ $3^5=243$

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

$x=\frac{3^{2n+2}}{3^{2n-}}=3^3=27$.