3.19. Вычислите: 1) \(\left((\sqrt{3})^2\right)^3\); 2) \(\left(-(-\sqrt{2})^2\right)^3\); 3) \(\left(-\frac{1}{5}(\sqrt{5})^2\right)^3\); 4) \(\left(-\frac{1}{2}(\sqrt{3})^{-1}\right)^6\).

1. \(\left((\sqrt{3})^2\right)^3=3^3=27\).
2. \(\left(-(-\sqrt{2})^2\right)^3=(-2)^3=-8\).
3. \(\left(-\frac15(\sqrt5)^2\right)^3=(-1)^3=-1\).
4. \(\left(-\frac12\cdot\frac1{\sqrt3}\right)^6=\left(-\frac1{2\sqrt3}\right)^6=\frac1{64\cdot27}=\frac1{1728}\).

Ответ: 1) 27; 2) −8; 3) −1; 4) \(\frac1{1728}\).