You may have rewritten the radical using a rational exponent, but then you applied that exponent only to the last factor. The expression can first be rewritten as: $\displaystyle{{\left({27}{{x}}^{{6}}{y}{{z}}^{{3}}\right)}}^{{\frac{{1}}{{3}}}}\usepackage{cmbright}\Huge\$

The second step is to write the expression as: $\displaystyle{{27}}^{{\frac{{1}}{{3}}}}\cdot{{\left({{x}}^{{6}}\right)}}^{{\frac{{1}}{{3}}}}\cdot{{\left({y}\right)}}^{{\frac{{1}}{{3}}}}\cdot{{\left({{z}}^{{3}}\right)}}^{{\frac{{1}}{{3}}}}\usepackage{cmbright}\Huge\$