Answer
$y\sqrt[3] {2y}$
Work Step by Step
$\sqrt[3] {54y^{4}}-y\sqrt[3] {16y}$
=$\sqrt[3] {2\times27\times y^{3}\times y}-y\sqrt[3] {8\times2y}$
=$(\sqrt[3] 2\times \sqrt[3] {27}\times \sqrt[3] {y^{3}}\times \sqrt[3] y)-y(\sqrt[3] 8\times\sqrt[3] {2y})$
=$(\sqrt[3] 2\times \sqrt[3] {3^{3}}\times \sqrt[3] {y^{3}}\times \sqrt[3] y)-y(\sqrt[3] {2^{3}}\times\sqrt[3] {2y})$
=$(\sqrt[3] 2\times 3\times y\times \sqrt[3] y)-y(2\times\sqrt[3] {2y})$
=$(3y\sqrt[3] {2y})-(2y\sqrt[3] {2y})$
=$(3y-2y)\sqrt[3] {2y}$
=$y\sqrt[3] {2y}$
