$ \sqrt{\frac {16^{10} + 8^{12}}{16^{5} + 8^8 }}=\sqrt{\frac {2^{40} + 2^{36}}{2^{20} + 2^{24} }} =\sqrt{\frac {2^{36} (1+ 2^{4})}{2^{20}(1+ 2^{4}) }}=\sqrt {2^{16}}=2^8=256$