Ответ:

  1. \(\sqrt[4]{81\cdot16}=\sqrt[4]{3^4\cdot2^4}=\sqrt[4]{6^4}=6\).
  2. \(\sqrt[3]{\frac{64}{27}}=\frac{\sqrt[3]{64}}{\sqrt[3]{27}}=\frac{4}{3}\).
  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. \(\sqrt[3]{\sqrt[3]{9^9}}=\sqrt[3]{9^3}=9\).