Упростите выражение [latex]\frac{5}{4+\sqrt{11}}+\frac{8}{\sqrt{19}-\sqrt{11}}-\frac{10}{\sqrt{19}+3}[/latex] Вычислите : [latex]9^{\frac{3}{2}}+27^{\frac{2}{3}}-(\frac{1}{16})^{-\frac{3}{4}}[/latex]

[latex]\frac{5}{4+\sqrt{11}}+\frac{8}{\sqrt{19}-\sqrt{11}}-\frac{10}{\sqrt{19}+3}=\frac{5(4-\sqrt{11})}{(4+\sqrt{11})(4-\sqrt{11})}+\frac{8(\sqrt{19}+\sqrt{11})}{(\sqrt{19}-\sqrt{11})(\sqrt{19}+\sqrt{11})}-\frac{10(\sqrt{19}-3)}{(\sqrt{19}+3)(\sqrt{19}-3)}=\frac{5(4-\sqrt{11})}{5}+\frac{8(\sqrt{19}+\sqrt{11})}{8}-\frac{10(\sqrt{19}-3)}{10}=4-\sqrt{11}+\sqrt{19}+\sqrt{11}-\sqrt{19}+3=4+3=7[/latex]   [latex]9^{\frac{3}{2}}+27^{\frac{2}{3}}-(\frac{1}{16})^{-\frac{3}{4}}=9^{\frac{3}{2}}+27^{\frac{2}{3}}-16^{\frac{3}{4}}=\sqrt[2]{9^3} +\sqrt[3]{27^2} -\sqrt[4]{16^3} =\sqrt[2]{9^3} +\sqrt[3]{27^2} -\sqrt[4]{16^3} =3^3+3^2-2^3=27+9-8=28[/latex]