69. Вычислить: 1) 2^(2−3√5)·8^√5; 2) 3^(1+2∛2):9^∛2; 3) (5^(1+√2))^(1−√2); 4) (5^(1−√5))^(1+√5)−(√5)^0.

1. \(2^{2-3\sqrt5}·8^{\sqrt5}=2^{2-3\sqrt5}·2^{3\sqrt5}=2^2=4\).
2. \(3^{1+2\sqrt[3]{2}}:9^{\sqrt[3]{2}}=3^{1+2\sqrt[3]{2}-2\sqrt[3]{2}}=3\).
3. \((5^{1+\sqrt2})^{1-\sqrt2}=5^{(1+\sqrt2)(1-\sqrt2)}=5^{-1}=\frac15\).
4. \((5^{1-\sqrt5})^{1+\sqrt5}-(\sqrt5)^0=5^{1-5}-1=\frac1{625}-1=-\frac{624}{625}\).

Ответ: 1) 4; 2) 3; 3) \(\frac15\); 4) \(-\frac{624}{625}\).