Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 38

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\[1)\ \sqrt[3]{2ab^{2}} \bullet \sqrt[3]{4a^{2}b} =\]

\[= \sqrt[3]{2ab^{2} \bullet 4a^{2}b} = \sqrt[3]{8a^{3}b^{3}} =\]

\[= \sqrt[3]{8} \bullet \sqrt[3]{a^{3}} \bullet \sqrt[3]{b^{3}} =\]

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

\[2)\ \sqrt[4]{3a^{2}b^{3}} \bullet \sqrt[4]{27a^{2}b} =\]

\[= \sqrt[4]{3a^{2}b^{3} \bullet 27a^{2}b} =\]

\[= \sqrt[4]{81a^{4}b^{4}} =\]

\[= \sqrt[4]{81} \bullet \sqrt[4]{a^{4}} \bullet \sqrt[4]{b^{4}} =\]

\[= \sqrt[4]{3^{4}} \bullet a \bullet b = 3ab\]

\[3)\ \sqrt[4]{\frac{\text{ab}}{c}} \bullet \sqrt[4]{\frac{a^{3}c}{b}} = \sqrt[4]{\frac{\text{ab}}{c} \bullet \frac{a^{3}c}{b}} =\]

\[= \sqrt[4]{a^{4}} = a\]

\[4)\ \sqrt[3]{\frac{16a}{b^{2}}} \bullet \sqrt[3]{\frac{1}{2ab}} = \sqrt[3]{\frac{16a}{b^{2}} \bullet \frac{1}{2ab}} =\]

\[= \sqrt[3]{\frac{8}{b^{3}}} = \sqrt[3]{8}\ :\sqrt[3]{b^{3}} =\]

\[= \sqrt[3]{2^{3}}\ :b = \frac{2}{b}\]