Question

The value of $\frac{{\left(243\right)}^{\frac{n}{5}}{.3}^{2n+1}}{9^n{.3}^{n-1}}$

• A. $1$
• B. $9$
• C. $3$
• D. $3^n$

Answer 1

The correct option is B $9$

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

$=\frac{3^n{.3}^{2n+1}}{3^{2n}{.3}^{n-1}}$

$=\frac{3^{3n+1}}{3^{3n-1}}$

$=3^{(3n+1)-(3n-1)}$

$=3^2=9$