\sqrt[4]{7 \frac{19}{32} }= \sqrt[4]{ \frac{243}{32}} =\frac{\sqrt[4]{3^5}}{\sqrt[4]{2^5}}=\frac{\sqrt[4]{3^4*3}}{\sqrt[4]{2^4*2}}=\frac{3\sqrt[4]3}{2\sqrt[4]2}=
=\frac{3\sqrt[4]3*\sqrt[4]8}{2\sqrt[4]2*\sqrt[4]8}=\frac{3\sqrt[4]{24}}{2\sqrt[4]{16}}=\frac{3\sqrt[4]{24}}{2*2}=\frac{3\sqrt[4]{24}}{4}