Factor 24 to find a perfect cube: $\displaystyle{\sqrt[{{3}}]{{{2}\cdot{2}\cdot{2}\cdot{3}\cdot{{c}}^{{16}}}}}={\sqrt[{{3}}]{{{{2}}^{{3}}\cdot{3}\cdot{{c}}^{{16}}}}}\usepackage{cmbright}\Huge\$

Factor $\displaystyle{{c}}^{{16}}\usepackage{cmbright}\Huge\$ to find a perfect cube: $\displaystyle={\sqrt[{{3}}]{{{{2}}^{{3}}\cdot{3}\cdot{{c}}^{{15}}\cdot{c}}}}={\sqrt[{{3}}]{{{{2}}^{{3}}\cdot{3}\cdot{{\left({{c}}^{{5}}\right)}}^{{3}}\cdot{c}}}}\usepackage{cmbright}\Huge\$

Rewrite as a product of radicals: $\displaystyle={\sqrt[{{3}}]{{{{2}}^{{3}}}}}\cdot{\sqrt[{{3}}]{{{3}}}}\cdot{\sqrt[{{3}}]{{{{\left({{c}}^{{5}}\right)}}^{{3}}}}}\cdot{\sqrt[{{3}}]{{{c}}}}\usepackage{cmbright}\Huge\$

Simplify and multiply: $\displaystyle={2}\cdot{{c}}^{{5}}\cdot{\sqrt[{{3}}]{{{3}}}}\cdot{\sqrt[{{3}}]{{{c}}}}={2}{{c}}^{{5}}{\sqrt[{{3}}]{{{3}{c}}}}\usepackage{cmbright}\Huge\$