You used the rules of exponents to simplify the expression: $\displaystyle{{\left({5}{{a}}^{{-{{2}}}}{{b}}^{{4}}{{c}}^{{3}}\right)}}^{{3}}\div{{\left({{5}}^{{2}}{{a}}^{{-{{3}}}}{{b}}^{{-{{2}}}}\right)}}^{{2}}=\frac{{{{b}}^{{16}}{{c}}^{{9}}}}{{5}}\usepackage{cmbright}\Huge\$ .