a)
\sqrt{5{\sqrt{5{\sqrt5}}}}=5^{\frac{1}{2}}*(5^{\frac{1}{2}})^{\frac{1}{2}}*((5^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}=5^{\frac{1}{2}}*5^{\frac{1}{4}}*5^{\frac{1}{8}}=5^{\frac{4+2+1}{8}}=5^{\frac{7}{8}}
b)
(64^{-5}*\frac{1}{256})^{2\frac{2}{3}}:(\sqrt[3]{1024}:4)=[(2^6)^{-5}*(\frac{1}{2})^8]^{\frac{8}{3}}: (\sqrt[3]{2^{10}}:2^2)=
(2^{-30}*2^{-8})^{\frac{8}{3}}:(2^{\frac{10}{3}}:2^2)=(2^{-38})^{\frac{8}{3}}:2^{\frac{10}{3}-\frac{6}{3}}=
2^{-\frac{304}{3}}:2^{\frac{4}{3}}=2^{\frac{-304-4}{3}}=2^{\frac{-308}{3}}