Simplify$\frac{(\frac{-3}{4})^{5} \times \frac{125}{27}} {[\frac{5}{3}\times{ 9}{16}]}$

Given: $\frac{(\frac{-3}{4})^{5} \times \frac{125}{27}} {[\frac{5}{3}\times{ 9}{16}]}$

To do:  Simplify the given expression.

Solution:

$\frac{(\frac{-3}{4})^{5} \times \frac{125}{27}} {[\frac{5}{3}\times{ 9}{16}]}$

=$(-1)^{5}$ $\times$ $\frac{243}{1024} \times \frac{125}{27} \times \frac{3}{5} \times {16}{9}$

= $ -1\frac{75}{64}$

= $ \frac{75}{64}$

Therefore, the answer is  $ \frac{75}{64}$