Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 82

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\[1)\ \frac{m^{\sqrt{3}} \bullet n^{\sqrt{3}}}{\left( \text{mn} \right)^{2 + \sqrt{3}}} = \frac{\left( \text{mn} \right)^{\sqrt{3}}}{\left( \text{mn} \right)^{2 + \sqrt{3}}} =\]

\[= \left( \text{mn} \right)^{\sqrt{3} - \left( 2 + \sqrt{3} \right)} = \left( \text{mn} \right)^{- 2} =\]

\[= \frac{1}{\left( \text{mn} \right)^{2}}\]

\[2)\ \frac{x^{\sqrt{7}} \bullet y^{\sqrt{7} + 1}}{\left( \text{xy} \right)^{\sqrt{7}}} = \frac{x^{\sqrt{7}} \bullet y^{\sqrt{7} + 1}\ }{x^{\sqrt{7}} \bullet y^{\sqrt{7}}} =\]

\[= x^{\sqrt{7} - \sqrt{7}} \bullet y^{\sqrt{7} + 1 - \sqrt{7}} = x^{0} \bullet y^{1} =\]

\[= 1 \bullet y = y\]

\[3)\ \left( a^{\sqrt{2}} - b^{\sqrt{3}} \right)\left( a^{\sqrt{2}} + b^{\sqrt{3}} \right) =\]

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

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

\[= \left( 2a^{- \frac{1}{2}} \right)^{2} - \left( \frac{1}{3}b^{- \sqrt{3}} \right)^{2} =\]

\[= 4a^{- 1} - \frac{1}{9}b^{- 2\sqrt{3}} = \frac{4}{a} - \frac{1}{9b^{2\sqrt{3}}}\]