5. Реши: 1) \(\sqrt[4]{81\cdot16}\); 2) \(\sqrt{\frac{64}{27}}\); 3) \(\sqrt{\sqrt[3]{4^6}}\); 4) \(\sqrt[3]{(\sqrt{50})^2-(\sqrt{23})^2}\); 5) \(\sqrt[3]{\sqrt[3]{9^9}}\).

1. \(\sqrt[4]{81\cdot16}=\sqrt[4]{3^4\cdot2^4}=\sqrt[4]{6^4}=6\).
2. \(\sqrt{\frac{64}{27}}=\frac{8}{3\sqrt3}=\frac{8\sqrt3}{9}\).
3. \(\sqrt{\sqrt[3]{4^6}}=\sqrt{4^2}=4\).
4. \(\sqrt[3]{(\sqrt{50})^2-(\sqrt{23})^2}=\sqrt[3]{50-23}=\sqrt[3]{27}=3\).
5. \(\sqrt[3]{\sqrt[3]{9^9}}=\sqrt[9]{9^9}=9\).

Ответ: 1) 6; 2) \(\frac{8\sqrt3}{9}\); 3) 4; 4) 3; 5) 9.