Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 480

\[\boxed{\mathbf{480}.}\]

\[1)\ 3^{\sqrt{5}} \bullet 3^{- \sqrt{5}} = 3^{\sqrt{5} - \sqrt{5}} = 3^{0} = 1;\]

\[2)\ 3^{2\sqrt{2}}\ :9^{\sqrt{2}} = 3^{2\sqrt{2}}\ :\left( 3^{2} \right)^{\sqrt{2}} =\]

\[= 3^{2\sqrt{2}}\ :3^{2\sqrt{2}} = 3^{2\sqrt{2} - 2\sqrt{2}} =\]

\[= 3^{0} = 1;\]

\[3)\ \left( 6^{\sqrt{3}} \right)^{\sqrt{3}} = 6^{\sqrt{3 \bullet 3}} = 6^{3} = 216;\]

\[4)\ \left( (0,5)^{\sqrt{2}} \right)^{\sqrt{8}} = (0,5)^{\sqrt{2 \bullet 8}} =\]

\[= (0,5)^{\sqrt{16}} = \left( \frac{1}{2} \right)^{\sqrt{4^{2}}} =\]

\[= \left( \frac{1}{2} \right)^{4} = \frac{1}{16} = 0,0625.\]