Simplify
${\left(25\right)}^{3/2}\times {\left(625\right)}^{-1/4}$

$(25{)}^{3/2}\times (625{)}^{-1/4}$

$25=5^2;625=5^4$

$(5^2{)}^{\frac{3}{2}}\times (5^4{)}^{-1/4}$

$5^3\times 5^{-1}=\frac{125}{5}$

$=25.$

$\therefore (25{)}^{3/2}\times (625{)}^{-1/4}=25$