#### Answer

$30y^2\sqrt[3]{2y}$

#### Work Step by Step

RECALL:
$\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a\cdot b}.$
Use the rule above to have
$6\sqrt[3]{(5y^3)(50y^4)}
\\=6\sqrt[3]{250y^7}
\\=6\sqrt[3]{125y^6(2y)}
\\=6\sqrt[3]{(5y^2)^3(2y)}
\\=6(5y^2)\sqrt[3]{2y}
\\=30y^2\sqrt[3]{2y}.$