Incorrect. Rewrite using $\displaystyle\frac{{{\sqrt[{{3}}]{{a}}}}}{{{\sqrt[{{3}}]{{b}}}}}={\sqrt[{{3}}]{{\frac{{a}}{{b}}}}}\usepackage{cmbright}\Huge\$ : $\displaystyle\frac{{\sqrt[{{3}}]{{{1},{024}{{x}}^{{6}}{{y}}^{{4}}}}}}{{\sqrt[{{3}}]{{{2}{{x}}^{{3}}{y}}}}}={\sqrt[{{3}}]{{\frac{{{1},{024}{{x}}^{{6}}{{y}}^{{4}}}}{{{2}{{x}}^{{3}}{y}}}}}}\usepackage{cmbright}\Huge\$

Identify common factors in the numerator and denominator and simplify. Identify perfect cubes and pull them out of the radical.