Реши примеры: a) 4^(0.6) * 2^(0.2) : 2^(-0.6); б) 3 * 9^(0.4) : ∜(5)(3^(-1)); в) 4^(1/3) * 2^(1 2/3) : 4^(-1/3); г) 8^(-1/3) * 16^(1/3) : ∜(3)(2)

Решим примеры по порядку: a) $4^{0.6} \cdot 2^{0.2} : 2^{-0.6} = (2^2)^{0.6} \cdot 2^{0.2} : 2^{-0.6} = 2^{1.2} \cdot 2^{0.2} : 2^{-0.6} = 2^{1.2 + 0.2 - (-0.6)} = 2^{1.2 + 0.2 + 0.6} = 2^2 = 4$ б) $3 \cdot 9^{0.4} : \sqrt[5]{3^{-1}} = 3 \cdot (3^2)^{0.4} : 3^{-\frac{1}{5}} = 3 \cdot 3^{0.8} : 3^{-0.2} = 3^{1 + 0.8 - (-0.2)} = 3^{1 + 0.8 + 0.2} = 3^2 = 9$ в) $4^{\frac{1}{3}} \cdot 2^{1\frac{2}{3}} : 4^{-\frac{1}{3}} = 4^{\frac{1}{3}} \cdot 2^{\frac{5}{3}} : 4^{-\frac{1}{3}} = (2^2)^{\frac{1}{3}} \cdot 2^{\frac{5}{3}} : (2^2)^{-\frac{1}{3}} = 2^{\frac{2}{3}} \cdot 2^{\frac{5}{3}} : 2^{-\frac{2}{3}} = 2^{\frac{2}{3} + \frac{5}{3} - (-\frac{2}{3})} = 2^{\frac{2}{3} + \frac{5}{3} + \frac{2}{3}} = 2^{\frac{9}{3}} = 2^3 = 8$ г) $8^{-\frac{1}{3}} \cdot 16^{\frac{1}{3}} : \sqrt[3]{2} = (2^3)^{-\frac{1}{3}} \cdot (2^4)^{\frac{1}{3}} : 2^{\frac{1}{3}} = 2^{-1} \cdot 2^{\frac{4}{3}} : 2^{\frac{1}{3}} = 2^{-1 + \frac{4}{3} - \frac{1}{3}} = 2^{-1 + \frac{3}{3}} = 2^{-1 + 1} = 2^0 = 1$ **Ответ:** а) 4 б) 9 в) 8 г) 1