Можешь вычислить значения выражений со степенями в заданиях 469-472?

Конечно, давай вычислим! Вот решения: 469. 1) $16^{\frac{1}{2}} = \sqrt{16} = 4$ 2) $27^{\frac{2}{3}} = (27^{\frac{1}{3}})^2 = (\sqrt[3]{27})^2 = 3^2 = 9$ 3) $8^{\frac{1}{3}} = \sqrt[3]{8} = 2$ 4) $64^{\frac{2}{3}} = (64^{\frac{1}{3}})^2 = (\sqrt[3]{64})^2 = 4^2 = 16$ 5) $16^{-0.75} = 16^{-\frac{3}{4}} = (16^{\frac{1}{4}})^{-3} = (\sqrt[4]{16})^{-3} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$ 6) $9^{-1.5} = 9^{-\frac{3}{2}} = (9^{\frac{1}{2}})^{-3} = (\sqrt{9})^{-3} = 3^{-3} = \frac{1}{3^3} = \frac{1}{27} \approx 0.037$ 470. 1) $2^{\frac{2}{5}} \cdot 2^{\frac{8}{5}} = 2^{\frac{2}{5} + \frac{8}{5}} = 2^{\frac{10}{5}} = 2^2 = 4$ 2) $5^{\frac{3}{8}} \cdot 5^{\frac{5}{8}} = 5^{\frac{3}{8} + \frac{5}{8}} = 5^{\frac{8}{8}} = 5^1 = 5$ 3) $4^{\frac{5}{6}} : 4^{\frac{1}{3}} = 4^{\frac{5}{6} - \frac{1}{3}} = 4^{\frac{5}{6} - \frac{2}{6}} = 4^{\frac{3}{6}} = 4^{\frac{1}{2}} = \sqrt{4} = 2$ 4) $9^{\frac{1}{3}} : 9^{\frac{5}{6}} = 9^{\frac{1}{3} - \frac{5}{6}} = 9^{\frac{2}{6} - \frac{5}{6}} = 9^{-\frac{3}{6}} = 9^{-\frac{1}{2}} = \frac{1}{9^{\frac{1}{2}}} = \frac{1}{\sqrt{9}} = \frac{1}{3} \approx 0.333$ 5) $(8^{\frac{1}{15}})^{-5} = 8^{\frac{1}{15} \cdot (-5)} = 8^{-\frac{5}{15}} = 8^{-\frac{1}{3}} = \frac{1}{8^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{8}} = \frac{1}{2} = 0.5$ 471. 1) $9^{\frac{2}{5}} \cdot 27^{\frac{2}{5}} = (3^2)^{\frac{2}{5}} \cdot (3^3)^{\frac{2}{5}} = 3^{\frac{4}{5}} \cdot 3^{\frac{6}{5}} = 3^{\frac{4}{5} + \frac{6}{5}} = 3^{\frac{10}{5}} = 3^2 = 9$ 2) $7^{\frac{2}{3}} \cdot 49^{\frac{2}{3}} = 7^{\frac{2}{3}} \cdot (7^2)^{\frac{2}{3}} = 7^{\frac{2}{3}} \cdot 7^{\frac{4}{3}} = 7^{\frac{2}{3} + \frac{4}{3}} = 7^{\frac{6}{3}} = 7^2 = 49$ 3) $144^{\frac{3}{4}} : 9^{\frac{3}{4}} = (144 : 9)^{\frac{3}{4}} = 16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^3 = 8$ 4) $150^{\frac{3}{2}} : 6^{\frac{3}{2}} = (150 : 6)^{\frac{3}{2}} = 25^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} = 5^3 = 125$ 472. 1) $(\frac{1}{81})^{-0.75} + (\frac{1}{27})^{-\frac{4}{3}} = (\frac{1}{3^4})^{-\frac{3}{4}} + (\frac{1}{3^3})^{-\frac{4}{3}} = (3^{-4})^{-\frac{3}{4}} + (3^{-3})^{-\frac{4}{3}} = 3^3 + 3^4 = 27 + 81 = 108$ 2) $(0.04)^{-1.5} - (0.125)^{\frac{2}{3}} = (\frac{4}{100})^{-\frac{3}{2}} - (\frac{125}{1000})^{\frac{2}{3}} = (\frac{1}{25})^{-\frac{3}{2}} - (\frac{1}{8})^{\frac{2}{3}} = (25)^{\frac{3}{2}} - (\frac{1}{8})^{\frac{2}{3}} = (5^2)^{\frac{3}{2}} - (\frac{1}{2^3})^{\frac{2}{3}} = 5^3 - (\frac{1}{2})^2 = 125 - \frac{1}{4} = 124.75$ 3) $10^{\frac{9}{7}} : 10^{\frac{2}{7}} - 5^{\frac{6}{5}} \cdot 5^{-\frac{4}{5}} = 10^{\frac{9}{7} - \frac{2}{7}} - 5^{\frac{6}{5} - \frac{4}{5}} = 10^{\frac{7}{7}} - 5^{\frac{2}{5}} = 10 - 5^{\frac{2}{5}} \approx 10 - 2.297 = 7.703$ 4) $(5^{-\frac{2}{5}})^{-5} + (0.2)^{-\frac{4}{3}} = 5^2 + (\frac{1}{5})^{-\frac{4}{3}} = 25 + (5)^{\frac{4}{3}} \approx 25 + 8.55 = 33.55$