To find the fifth root, identify all fifth roots within the radical: $\displaystyle{\sqrt[{{5}}]{{{192}{{a}}^{{7}}{{b}}^{{12}}{{c}}^{{11}}}}}={\sqrt[{{5}}]{{{{2}}^{{5}}\cdot{6}\cdot{{a}}^{{5}}\cdot{{a}}^{{2}}\cdot{{\left({{b}}^{{2}}\right)}}^{{5}}\cdot{{b}}^{{2}}\cdot{{\left({{c}}^{{2}}\right)}}^{{5}}\cdot{c}}}}\usepackage{cmbright}\Huge\$ . Then pull out the roots and simplify the expression: $\displaystyle{2}{a}{{b}}^{{2}}{{c}}^{{2}}{\sqrt[{{5}}]{{{6}{{a}}^{{2}}{{b}}^{{2}}{c}}}}\usepackage{cmbright}\Huge\$ .