Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 470

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\[1)\ 2^{\frac{2}{5}} \bullet 2^{\frac{8}{5}} = 2^{\frac{10}{5}} = 2^{2} = 4;\]

\[2)\ 5^{\frac{3}{8}} \bullet 5^{\frac{5}{8}} = 5^{\frac{8}{8}} = 5^{1} = 5;\]

\[3)\ 4^{\frac{5}{6}}\ :4^{\frac{1}{3}} = 4^{\frac{5 - 2}{6}} = 4^{\frac{3}{6}} =\]

\[= 4^{\frac{1}{2}} = \left( 2^{2} \right)^{\frac{1}{2}} = 2;\]

\[4)\ 9^{\frac{1}{3}}\ :9^{\frac{5}{6}} = 9^{\frac{2 - 5}{6}} = 9^{- \frac{3}{6}} = 9^{- \frac{1}{2}} =\]

\[= \left( 3^{2} \right)^{- \frac{1}{2}} = 3^{- 1} = \frac{1}{3};\]

\[5)\ \left( 8^{\frac{1}{15}} \right)^{- 5} = 8^{- \frac{5}{15}} = 8^{- \frac{1}{3}} =\]

\[= \left( 2^{3} \right)^{- \frac{1}{3}} = 2^{- 1} = \frac{1}{2}.\]