Вычисление выражений

• а) $$4^{\frac{1}{3}} \cdot 4 \div 4^{\frac{1}{6}} = 4^{\frac{1}{3}} \cdot 4^1 \cdot 4^{-\frac{1}{6}} = 4^{\frac{1}{3} + 1 - \frac{1}{6}} = 4^{\frac{2+6-1}{6}} = 4^{\frac{7}{6}} = (2^2)^{\frac{7}{6}} = 2^{\frac{14}{6}} = 2^{\frac{7}{3}} = \sqrt[3]{2^7} = \sqrt[3]{128}$$
• б) $$27^{\frac{1}{2}} \cdot (3^{-\frac{1}{4}})^2 = (3^3)^{\frac{1}{2}} \cdot 3^{-\frac{2}{4}} = 3^{\frac{3}{2}} \cdot 3^{-\frac{1}{2}} = 3^{\frac{3}{2} - \frac{1}{2}} = 3^{\frac{2}{2}} = 3^1 = 3$$