\( \sqrt[3]{\frac{125 x^{9}}{27 y^{3}}} \)

Step 1 ：\( \sqrt[3]{\frac{125 x^{9}}{27 y^{3}}} = \frac{\sqrt[3]{125 x^{9}}}{\sqrt[3]{27 y^{3}}} \)

Step 2 ：\( \frac{\sqrt[3]{125 x^{9}}}{\sqrt[3]{27 y^{3}}} = \frac{5 x^{3}}{3 y} \)

Step 3 ：\( \frac{5 x^{3}}{3 y} \)