Применяем свойства степеней: \(64^{\frac{3}{4}} = (64^{\frac{1}{4}})^3\). Поскольку \(64 = 2^6\), то \(64^{\frac{1}{4}} = 2^{\frac{6}{4}} = 2^{\frac{3}{2}} = 2 \cdot \sqrt{2}\). Итак: \(64^{\frac{3}{4}} = (2 \cdot \sqrt{2})^3 = 8 \cdot 2\sqrt{2} = 16\sqrt{2}\).