$\frac{{{\left( 0/5 \right)}^{-3}}\times {{\left( 0/125 \right)}^{-4}}}{{{\left( 0/25 \right)}^{3}}\times {{\left( 0/625 \right)}^{4}}\times {{2}^{16}}}=\frac{{{\left( \frac{5}{10} \right)}^{-3}}}{{{\left( \frac{25}{100} \right)}^{3}}}\times \frac{{{\left( \frac{125}{1000} \right)}^{-4}}}{{{\left( \frac{625}{10000} \right)}^{4}}}\times \frac{1}{{{2}^{16}}}=\frac{{{\left( \frac{10}{5} \right)}^{-3}}}{{{\left( \frac{25}{100} \right)}^{3}}}\times \frac{{{\left( \frac{1000}{125} \right)}^{4}}}{{{\left( \frac{625}{10000} \right)}^{4}}}=\frac{1}{\left( {{2}^{4}} \right)}={{\left( \frac{1000}{125} \right)}^{3}}\times {{\left( \frac{8}{\frac{1}{16}} \right)}^{4}}\times \left( \frac{1}{{{16}^{4}}} \right)={{8}^{3}}\times \frac{{{8}^{4}}\times {{16}^{4}}}{{{16}^{4}}}={{8}^{3}}\times {{8}^{4}}={{8}^{7}}$