ABC26GN1900 · Surds and Indices

Let $9^{3} \times(81)^{2} \div(27)^{3}=3^{x}$. Then, $$\begin{aligned} & 3^{x}=\frac{\left(3^{2}\right)^{3} \times\left(3^{4}\right)^{2}}{\left(3^{3}\right)^{3}}=\frac{3^{(2 \times 3)} \times 3^{(4 \times 2)}}{3^{(3 \times 3)}}=\frac{3^{6} \times 3^{8}}{3^{9}}=\frac{3^{(6+8)}}{3^{9}} \\ & \Rightarrow 3^{x}=\frac{3^{14}}{3^{9}}=3^{(14-9)}=3^{5} \Rightarrow x=5 . \end{aligned}$$