You have used the wrong order of operations. This would have been the answer if the problem was to simplify $\displaystyle{{\left(-{c}\cdot{{c}}^{{4}}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ . You have to apply exponents before multiplication. So in the original expression you should simplify $\displaystyle{{\left({{c}}^{{4}}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ first, and then use the product rule.