Correct. You applied the rules of exponents correctly to simplify this expression. $\displaystyle{{9}}^{{-{{3}}}}\cdot{{3}}^{{4}}\cdot{{\left({27}\right)}}^{{8}}={{\left({{3}}^{{2}}\right)}}^{{-{{3}}}}\cdot{{3}}^{{4}}\cdot{{\left({{3}}^{{3}}\right)}}^{{8}}={{3}}^{{-{{6}}}}\cdot{{3}}^{{4}}\cdot{{3}}^{{24}}\usepackage{cmbright}\Huge\$ which simplifies to $\displaystyle{{3}}^{{22}}\usepackage{cmbright}\Huge\$ .