The expression $\displaystyle{{4}}^{{9}}\cdot{{\left({{\left({64}\right)}}^{{-{{2}}}}\cdot{{4}}^{{8}}\right)}}^{{-{{2}}}}\usepackage{cmbright}\Huge\$ can be simplified to be a power of 4. If 4 is the base in this new expression, what is the exponent? (You might find the fact $\displaystyle{64}={{4}}^{{3}}\usepackage{cmbright}\Huge\$ useful.)