Можешь ли ты помочь решить примеры 58-60?

Конечно, давай разберёмся с этими заданиями! Выглядят они немного сложно, но мы справимся. **58** 1) $2^{\frac{4}{5}} \cdot 2^{\frac{11}{5}} = 2^{\frac{4}{5} + \frac{11}{5}} = 2^{\frac{15}{5}} = 2^3 = 8$ 2) $5^{\frac{2}{7}} \cdot 5^{\frac{5}{7}} = 5^{\frac{2}{7} + \frac{5}{7}} = 5^{\frac{7}{7}} = 5^1 = 5$ 3) $9^{\frac{2}{3}} : 9^{\frac{1}{6}} = 9^{\frac{2}{3} - \frac{1}{6}} = 9^{\frac{4}{6} - \frac{1}{6}} = 9^{\frac{3}{6}} = 9^{\frac{1}{2}} = \sqrt{9} = 3$ 4) $4^{\frac{1}{3}} : 4^{\frac{5}{6}} = 4^{\frac{1}{3} - \frac{5}{6}} = 4^{\frac{2}{6} - \frac{5}{6}} = 4^{-\frac{3}{6}} = 4^{-\frac{1}{2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}$ 5) $(8^{\frac{1}{12}})^{-4} = 8^{\frac{1}{12} \cdot (-4)} = 8^{-\frac{4}{12}} = 8^{-\frac{1}{3}} = \frac{1}{\sqrt[3]{8}} = \frac{1}{2}$ **59** 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) $144^{\frac{3}{4}} : 9^{\frac{3}{4}} = (144:9)^{\frac{3}{4}} = 16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8$ 4) $150^{\frac{3}{2}} : 6^{\frac{3}{2}} = (150:6)^{\frac{3}{2}} = 25^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} = 5^{2 \cdot \frac{3}{2}} = 5^3 = 125$ **60** 1) $(\frac{1}{16})^{-0.75} + (\frac{1}{8})^{-\frac{4}{3}} = (\frac{1}{16})^{-\frac{3}{4}} + (\frac{1}{8})^{-\frac{4}{3}} = 16^{\frac{3}{4}} + 8^{\frac{4}{3}} = (2^4)^{\frac{3}{4}} + (2^3)^{\frac{4}{3}} = 2^3 + 2^4 = 8 + 16 = 24$ 2) $(0.04)^{-1.5} - (0.125)^{-\frac{2}{3}} = (\frac{4}{100})^{-\frac{3}{2}} - (\frac{125}{1000})^{-\frac{2}{3}} = (\frac{1}{25})^{\frac{-3}{2}} - (\frac{1}{8})^{\frac{-2}{3}} = 25^{\frac{3}{2}} - 8^{\frac{2}{3}} = (5^2)^{\frac{3}{2}} - (2^3)^{\frac{2}{3}} = 5^3 - 2^2 = 125 - 4 = 121$ 3) $8^{\frac{9}{7}} \cdot 8^{\frac{2}{7}} - 3^{\frac{6}{5}} \cdot 3^{\frac{4}{5}} = 8^{\frac{9}{7} + \frac{2}{7}} - 3^{\frac{6}{5} + \frac{4}{5}} = 8^{\frac{11}{7}} - 3^{\frac{10}{5}} = 8^{\frac{11}{7}} - 3^2 = 8^{\frac{11}{7}} - 9$ 4) $(5^{-\frac{2}{5}})^{-5} + (0.2)^{-4} = 5^{(-\frac{2}{5}) \cdot (-5)} + (\frac{2}{10})^{-4} = 5^2 + (\frac{1}{5})^{-4} = 25 + 5^4 = 25 + 625 = 650$ Надеюсь, теперь тебе всё понятно! Если что, спрашивай ещё!