Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 36

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\[1)\ \sqrt[5]{3^{10} \bullet 2^{15}} = \sqrt[5]{3^{10}} \bullet \sqrt[5]{2^{15}} =\]

\[= \sqrt[5]{3^{5 \bullet 2}} \bullet \sqrt[5]{2^{5 \bullet 3}} = 3^{2} \bullet 2^{3} =\]

\[= 9 \bullet 8 = 72\]

\[2)\ \sqrt[3]{2^{3} \bullet 5^{6}} = \sqrt[3]{2^{3}} \bullet \sqrt[3]{5^{6}} =\]

\[= 2 \bullet \sqrt[3]{5^{3 \bullet 2}} = 2 \bullet 5^{2} = 2 \bullet 25 =\]

\[= 50\]

\[3)\ \sqrt[4]{3^{12} \bullet \left( \frac{1}{3} \right)^{8}} =\]

\[= \sqrt[4]{3^{12}} \bullet \sqrt[4]{\left( \frac{1}{3} \right)^{8}} =\]

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

\[= 27 \bullet \frac{1}{9} = 3\]

\[4)\ \sqrt[10]{4^{30} \bullet \left( \frac{1}{2} \right)^{20}} =\]

\[= \sqrt[10]{4^{30}} \bullet \sqrt[10]{\left( \frac{1}{2} \right)^{20}} =\]

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

\[= 4^{3} \bullet \left( \frac{1}{2} \right)^{2} = 64 \bullet \frac{1}{4} = 16\]