Rewrite the radical with a rational exponent: $\displaystyle{{\left({27}{{x}}^{{6}}{y}{{z}}^{{3}}\right)}}^{{\frac{{1}}{{3}}}}\usepackage{cmbright}\Huge\$

Use the laws of exponents to rewrite the expression: $\displaystyle{{27}}^{{\frac{{1}}{{3}}}}\cdot{{x}}^{{\frac{{6}}{{3}}}}\cdot{{y}}^{{\frac{{1}}{{3}}}}\cdot{{z}}^{{\frac{{3}}{{3}}}}\usepackage{cmbright}\Huge\$

Write $\displaystyle{27}={3}\cdot{3}\cdot{3}={{3}}^{{3}}\usepackage{cmbright}\Huge\$ , and simplify exponents: $\displaystyle{{\left({{3}}^{{3}}\right)}}^{{\frac{{1}}{{3}}}}{{x}}^{{2}}{{y}}^{{\frac{{1}}{{3}}}}{z}={3}{{x}}^{{2}}{{y}}^{{\frac{{1}}{{3}}}}{z}\usepackage{cmbright}\Huge\$

Change $\displaystyle{{y}}^{{\frac{{1}}{{3}}}}\usepackage{cmbright}\Huge\$ to radical form: $\displaystyle{3}{{x}}^{{2}}{z}{\sqrt[{{3}}]{{{y}}}}\usepackage{cmbright}\Huge\$