2^(2-3√5)8^√5 = 2^(2-3√5)(2^3)^√5 = 2^(2-3√5)*2^(3√5) = 2^(2-3√5+3√5) = 2^2 = 4
(5^(1+√2))^(1-√2) = 5^(1-√2+√2-2) = 5^-1 = 1/5
2^(2-3√5)8^√5 = 2^(2-3√5)(2^3)^√5 = 2^(2-3√5)*2^(3√5) = 2^(2-3√5+3√5) = 2^2 = 4
(5^(1+√2))^(1-√2) = 5^(1-√2+√2-2) = 5^-1 = 1/5