Apply the exponent 3 to each factor in the first expression: $\displaystyle{{4}}^{{3}}{{a}}^{{3}}{{\left({{b}}^{{2}}\right)}}^{{3}}{\left(-{2}{{a}}^{{5}}\right)}\usepackage{cmbright}\Huge\$

Calculate $\displaystyle{{4}}^{{3}}\usepackage{cmbright}\Huge\$ and use the power rule to cube $\displaystyle{{b}}^{{2}}\usepackage{cmbright}\Huge\$ : $\displaystyle{64}{{a}}^{{3}}{{b}}^{{6}}{\left(-{2}{{a}}^{{5}}\right)}\usepackage{cmbright}\Huge\$

Multiply the coefficients and use the product rule: $\displaystyle-{128}{{a}}^{{8}}{{b}}^{{6}}\usepackage{cmbright}\Huge\$