Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 59

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\[1)\ 9^{\frac{2}{5}} \bullet 27^{\frac{2}{5}} = (9 \bullet 27)^{\frac{2}{5}} =\]

\[= \left( 3^{2} \bullet 3^{3} \right)^{\frac{2}{5}} = \left( 3^{5} \right)^{\frac{2}{5}} = 3^{2} = 9\]

\[2)\ 7^{\frac{2}{3}} \bullet 49^{\frac{2}{3}} = (7 \bullet 49)^{\frac{2}{3}} =\]

\[= \left( 7 \bullet 7^{2} \right)^{\frac{2}{3}} = \left( 7^{3} \right)^{\frac{2}{3}} = 7^{2} = 49\]

\[3)\ 144^{\frac{3}{4}}\ :9^{\frac{3}{4}} = \left( \frac{144}{9} \right)^{\frac{3}{4}} = (16)^{\frac{3}{4}} =\]

\[= \left( 2^{4} \right)^{\frac{3}{4}} = 2^{3} = 8\]

\[4)\ 150^{\frac{3}{2}}\ :6^{\frac{3}{2}} = \left( \frac{150}{6} \right)^{\frac{3}{2}} = (25)^{\frac{3}{2}} =\]

\[= \left( 5^{2} \right)^{\frac{3}{2}} = 5^{3} = 125\]