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

Calculate $\displaystyle{{5}}^{{2}}\usepackage{cmbright}\Huge\$ and use the power rule twice: $\displaystyle{25}{{a}}^{{8}}{{b}}^{{4}}{\left(-{3}{{b}}^{{4}}\right)}\usepackage{cmbright}\Huge\$

Multiply the coefficients and use the product rule: $\displaystyle-{75}{{a}}^{{8}}{{b}}^{{8}}\usepackage{cmbright}\Huge\$