The expression $\displaystyle{{\left({{4}}^{{-{{5}}}}{{2}}^{{8}}\right)}}^{{-{{2}}}}\usepackage{cmbright}\Huge\$ can be simplified to be a power of 2. If 2 is the base in this new expression, what is the exponent? (You might find the fact $\displaystyle{4}={{2}}^{{2}}\usepackage{cmbright}\Huge\$ useful.)