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

Calculate $\displaystyle{{2}}^{{3}}\usepackage{cmbright}\Huge\$ and use the power rule twice: $\displaystyle{8}{{a}}^{{9}}{{b}}^{{3}}{\left(-{2}{{b}}^{{4}}\right)}\usepackage{cmbright}\Huge\$

Multiply the coefficients and use the product rule: $\displaystyle-{16}{{a}}^{{9}}{{b}}^{{7}}\usepackage{cmbright}\Huge\$