Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 44

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\[1)\ \left( \sqrt[3]{x} \right)^{6} = \sqrt[3]{x^{6}} = \sqrt[3]{x^{3 \bullet 2}} = x^{2}\]

\[2)\ \left( \sqrt[3]{y^{2}} \right)^{3} = \sqrt[3]{\left( y^{2} \right)^{3}} = y^{2}\]

\[3)\ \left( \sqrt{a} \bullet \sqrt[3]{b} \right)^{6} = \sqrt{a^{6}} \bullet \sqrt[3]{b^{6}} =\]

\[= \sqrt{a^{2 \bullet 3}} \bullet \sqrt[3]{b^{3 \bullet 2}} = a^{3}b^{2}\]

\[4)\ \left( \sqrt[3]{a^{2}} \bullet \sqrt[4]{b^{3}} \right)^{12} =\]

\[= \sqrt[3]{\left( a^{2} \right)^{12}} \bullet \sqrt[4]{\left( b^{3} \right)^{12}} =\]

\[= \sqrt[3]{a^{24}} \bullet \sqrt[4]{b^{36}} = \sqrt[3]{a^{3 \bullet 8}} \bullet \sqrt[4]{b^{4 \bullet 9}} =\]

\[{= a^{8}b^{9} }{5)\ \left( \sqrt{\sqrt[3]{a^{2}b}} \right)^{6} = \left( \sqrt[{2 \bullet 3}]{a^{2}b} \right)^{6} =}\]

\[= \sqrt[6]{\left( a^{2}b \right)^{6}} = a^{2}b\]

\[6)\ \left( \sqrt[3]{\sqrt[4]{27a^{3}}} \right)^{4} = \left( \sqrt[{3 \bullet 4}]{27a^{3}} \right)^{4} =\]

\[= \sqrt[{3 \bullet 4}]{\left( 27a^{3} \right)^{4}} = \sqrt[3]{27a^{3}} =\]

\[= \sqrt[3]{3^{3}a^{3}} = 3a\]