\[\sqrt[4]{80x^{8}y^{12}} =\]
\[= \sqrt[4]{2^{4} \cdot 5 \cdot \left( x^{2} \right)^{4} \cdot \left( y^{3} \right)^{4}} =\]
\[= 2x^{2}\left| y^{3} \right| \cdot \sqrt[4]{5} = - 2\sqrt[4]{5}x^{2}y^{3}\]