Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 474

\[\boxed{\mathbf{474}.}\]

\[1)\ a^{\frac{1}{3}} \bullet \sqrt{a} = a^{\frac{1}{3}} \bullet a^{\frac{1}{2}} = a^{\frac{1}{3} + \frac{1}{2}} =\]

\[= a^{\frac{2 + 3}{6}} = a^{\frac{5}{6}};\]

\[2)\ b^{\frac{1}{2}} \bullet b^{\frac{1}{3}} \bullet \sqrt[6]{b} = b^{\frac{1}{2}} \bullet b^{\frac{1}{3}} \bullet b^{\frac{1}{6}} =\]

\[= b^{\frac{1}{2} + \frac{1}{3} + \frac{1}{6}} = b^{\frac{3 + 2 + 1}{6}} = b^{\frac{6}{6}} =\]

\[= b^{1} = b;\]

\[3)\ \sqrt[3]{b}\ :b^{\frac{1}{6}} = b^{\frac{1}{3}}\ :b^{\frac{1}{6}} = b^{\frac{1}{3} - \frac{1}{6}} =\]

\[= b^{\frac{2 - 1}{6}} = b^{\frac{1}{6}};\]

\[4)\ a^{\frac{4}{3}}\ :\ \sqrt[3]{a} = a^{\frac{4}{3}}\ :a^{\frac{1}{3}} = a^{\frac{4}{3} - \frac{1}{3}} =\]

\[= a^{\frac{3}{3}} = a^{1} = a;\]