Identifying the fifth roots under the radical, you find: $\displaystyle{\sqrt[{{5}}]{{{128}{{a}}^{{21}}{{b}}^{{13}}{{c}}^{{27}}}}}={\sqrt[{{5}}]{{{{2}}^{{5}}\cdot{4}\cdot{{\left({{a}}^{{4}}\right)}}^{{5}}\cdot{a}\cdot{{\left({{b}}^{{2}}\right)}}^{{5}}\cdot{{b}}^{{3}}\cdot{{\left({{c}}^{{5}}\right)}}^{{5}}\cdot{{c}}^{{2}}}}}\usepackage{cmbright}\Huge\$ . Pulling out the fifth roots, this simplifies to: $\displaystyle{2}{{a}}^{{4}}{{b}}^{{2}}{{c}}^{{5}}{\sqrt[{{5}}]{{{4}{a}{{b}}^{{3}}{{c}}^{{2}}}}}\usepackage{cmbright}\Huge\$ .