$$\sqrt {\frac{{16}}{{25}}} \times \sqrt {\frac{?}{{25}}} \times \frac{{16}}{{25}} = \frac{{256}}{{625}}$$

$$\eqalign{ & {\text{Let}}, \cr & \sqrt {\frac{{16}}{{25}}} \times \sqrt {\frac{x}{{25}}} \times \frac{{16}}{{25}} = \frac{{256}}{{625}} \cr & {\text{Then}}, \cr & \frac{4}{5} \times \frac{{\sqrt x }}{5} \times \frac{{16}}{{25}} = \frac{{256}}{{625}} \cr & \Leftrightarrow \frac{{64\sqrt x }}{{625}} = \frac{{256}}{{625}} \cr & \Leftrightarrow \sqrt x = \frac{{256}}{{625}} \times \frac{{625}}{{64}} \cr & \Leftrightarrow x = {4^2} \cr & \Leftrightarrow x = 16 \cr} $$