Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 68

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\[1)\ 2^{\sqrt{5}} \bullet 2^{- \sqrt{5}} = 2^{\sqrt{5} + \left( - \sqrt{5} \right)} =\]

\[= 2^{\sqrt{5} - \sqrt{5}} = 2^{0} = 1\]

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

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

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

\[3)\ \left( 5^{\sqrt{3}} \right)^{\sqrt{3}} = 5^{\sqrt{3 \bullet 3}} = 5^{\sqrt{3^{2}}} =\]

\[= 5^{3} = 125\]

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

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

\[= \frac{1}{16}\]