$\begin{array}{l}\text{Here,\hspace{0.17em}}\frac{2^4\times 2^5}{3^2\times 3^3\times 3^4}\\ \\ \left[\begin{array}{l}\because 16=2^4,32=2^5\\ 9=3^2,27=3^3\\ 81=3^4\end{array}\right]\\ \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}By applying the rule of indices,}\\ \\ \text{\hspace{0.17em}= \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{2^9}{3^9}={\left(\frac{2}{3}\right)}^9\end{array}$

Hence, Option D is correct.