It appears that you treated the cube root as if it were a square root. First rewrite using fractional exponents, then apply the laws of exponents:

$\displaystyle\frac{{{2}{x}{{\left({64}{{x}}^{{6}}{{y}}^{{5}}\right)}}^{{\frac{{1}}{{3}}}}}}{{{{x}}^{{2}}{{\left({16}{{y}}^{{2}}\right)}}^{{\frac{{1}}{{2}}}}}}=\frac{{{2}\cdot{x}\cdot{{64}}^{{\frac{{1}}{{3}}}}\cdot{{x}}^{{\frac{{6}}{{3}}}}\cdot{{y}}^{{\frac{{5}}{{3}}}}}}{{{{x}}^{{2}}\cdot{{16}}^{{\frac{{1}}{{2}}}}\cdot{{y}}^{{\frac{{2}}{{2}}}}}}\usepackage{cmbright}\Huge\$

Simplify exponents and calculate the roots of the constants.