Question

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

• A. 1
• B. 3
• C. 9
• D. 3ⁿ
• E. 27

Answer 1

The correct option is C

9

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