Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 491

\[\boxed{\mathbf{491}.}\]

\[1)\ \left( 2^{\frac{5}{3}} \bullet 5^{- \frac{1}{3}} - 5^{\frac{5}{3}} \bullet 2^{- \frac{1}{3}} \right) \bullet \sqrt[3]{10} =\]

\[= \left( 2^{\frac{5}{3}} \bullet 5^{- \frac{1}{3}} - 5^{\frac{5}{3}} \bullet 2^{- \frac{1}{3}} \right) \bullet\]

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

\[= 2^{\frac{5}{3} + \frac{1}{3}} \bullet 5^{- \frac{1}{3} + \frac{1}{3}} - 5^{\frac{5}{3} + \frac{1}{3}} \bullet 2^{- \frac{1}{3} + \frac{1}{3}} =\]

\[= 2^{2} \bullet 5^{0} - 5^{2} \bullet 2^{0} =\]

\[= 4 - 25 = - 21;\]

\[2)\ \left( 5^{\frac{1}{4}}\ :2^{\frac{3}{4}} - 2^{\frac{1}{4}}\ :5^{\frac{3}{4}} \right) \bullet \sqrt[4]{1000} =\]

\[= \left( 5^{\frac{1}{4}} \bullet 2^{- \frac{3}{4}} - 2^{\frac{1}{4}} \bullet 5^{- \frac{3}{4}} \right) \bullet \sqrt[4]{10^{3}} =\]

\[= \left( 5^{\frac{1}{4}}\ \bullet 2^{- \frac{3}{4}} - 2^{\frac{1}{4}} \bullet 5^{- \frac{3}{4}} \right) \bullet\]

\[\bullet (5 \bullet 2)^{\frac{3}{4}} = 5^{\frac{1}{4} + \frac{3}{4}} \bullet 2^{- \frac{3}{4} + \frac{3}{4}} -\]

\[- 2^{\frac{1}{4} + \frac{3}{4}} \bullet 5^{- \frac{3}{4} + \frac{3}{4}} = \ \]

\[= 5^{1} \bullet 2^{0} - 2^{1} \bullet 5^{0} = 5 - 2 = 3.\]