42. Вычислите: 1) \(\left(\sqrt[6]{7^3}\right)^2\); 2) \(\left(\sqrt[6]{9}\right)^{-3}\); 3) \(\left(\sqrt[10]{32}\right)^2\); 4) \(\left(\sqrt[8]{16}\right)^{-4}\).

1. \(\left(\sqrt[6]{7^3}\right)^2=\left(7^{\frac{3}{6}}\right)^2=7^1=7\).
2. \(\left(\sqrt[6]{9}\right)^{-3}=\left(9^{\frac{1}{6}}\right)^{-3}=9^{-\frac{1}{2}}=\frac{1}{\sqrt{9}}=\frac{1}{3}\).
3. \(\left(\sqrt[10]{32}\right)^2=\left(32^{\frac{1}{10}}\right)^2=32^{\frac{1}{5}}=2\), так как \(32=2^5\).
4. \(\left(\sqrt[8]{16}\right)^{-4}=\left(16^{\frac{1}{8}}\right)^{-4}=16^{-\frac{1}{2}}=\frac{1}{\sqrt{16}}=\frac{1}{4}\).

Ответ: 1) 7; 2) \(\frac{1}{3}\); 3) 2; 4) \(\frac{1}{4}\).