Answer
$3x^{2}y^{2}\sqrt[3] {2y^{2}}$
Work Step by Step
$\sqrt[3] {54x^{6}y^{8}}$
=$\sqrt[3] {2\times27\times x^{6}\times y^{6}\times y^{2}}$
=$\sqrt[3] {2\times3^{3}\times x^{6}\times y^{6}\times y^{2}}$
=$\sqrt[3] {3^{3}\times x^{6}\times y^{6}\times 2\times y^{2}}$
=$\sqrt[3] {3^{3}\times x^{6}\times y^{6}}\times \sqrt[3] {2\times y^{2}}$
=$3x^{2}y^{2}\times \sqrt[3] {2\times y^{2}}$
=$3x^{2}y^{2}\sqrt[3] {2y^{2}}$