#### Answer

$\color{blue}{(35x^2y^3-54x^2y^2)\sqrt[3]{z^2}}$

#### Work Step by Step

Factor each radicand so that at least one factor is a perfect cube, then then bring out the cube root of the perfect cube factors to obtain:
$=7\sqrt[3]{5^3(x^2)^3(y^3)^3(z^2)}-9x^2y\sqrt[3]{6^3y^3(z^2)}
\\=7(5x^2y^3)\sqrt[3]{z^2}-9x^2y(6y)\sqrt[3]{z^2}
\\=35x^2y^3\sqrt[3]{z^2}-54x^2y^2\sqrt[3]{z^2}$
Combine like terms to obtain:
$=\color{blue}{(35x^2y^3-54x^2y^2)\sqrt[3]{z^2}}$