9^3 × ( 81 )^2 ÷ ( 27 )^3 = ( 3 )^?

Answer: Option C

$$\begin{array}{rl}& \text{Let}{9}^3\times {\left(81\right)}^2÷{\left(27\right)}^3={\left(3\right)}^x\text{then}\\ & \Rightarrow {\left(3\right)}^x\text{ = }\frac{{\left(3^2\right)}^3\times {\left(3^4\right)}^2}{{\left(3^3\right)}^3}\\ & \Rightarrow {\left(3\right)}^x=\frac{3^{\left(2\times 3\right)}\times 3^{\left(4\times 2\right)}}{3^{\left(3\times 3\right)}}\\ & \Rightarrow {\left(3\right)}^x=\frac{3^6\times 3^8}{3^9}\\ & \Rightarrow {\left(3\right)}^x=\frac{3^{\left(6+8\right)}}{3^9}\\ & \Rightarrow {\left(3\right)}^x=\frac{3^{14}}{3^9}\\ & \Rightarrow {\left(3\right)}^x=3^{\left(14-9\right)}\\ & \Rightarrow {\left(3\right)}^x=3^5\\ & \Rightarrow {\left(3\right)}^x=5\end{array}$$