Question

ПОМОГИТЕ ПОЖАЛУЙСТА С ПРИМЕРАМИ ЗАДАНИЙ 1-2
ДАМ 50 БАЛЛОВ

Answer 1

$1)7^{(\sqrt{5}+1)^{2}}:7^{2\sqrt{5}}=7^{(\sqrt{5}+1)^{2}-2\sqrt{5}} =7^{5+2\sqrt{5}+1-2\sqrt{5}}=7^{6}=117649\\\\2)\sqrt[5]{7^{(\sqrt{3}+\sqrt{2})^{2}}*7^{(\sqrt{3}-\sqrt{2})^{2}}}=\sqrt[5]{7^{3+2\sqrt{6}+2+3-2\sqrt{6}+1}}=\sqrt[5]{7^{10}}=\sqrt[5]{(7^{2})^{5}}=7^{2}=49\\\\3)((\sqrt{6} )^{\sqrt{5}})^{\sqrt{5}}=(\sqrt{6})^{\sqrt{5}*\sqrt{5}}=(\sqrt{6})^{5}=36\sqrt{6}$

$4)(1\frac{4}{5})^{-2,25} =(\frac{9}{5} )^{-2,25}=(\frac{5}{9})^{2,25}\\\\\sqrt{5}<2,25\Rightarrow (\frac{5}{9})^{\sqrt{5}}}>(\frac{5}{9})^{2,25}\\\\5)(5+2\sqrt{6})^{-5,2}=(\frac{1}{5+2\sqrt{6} })^{5,2}=(5-2\sqrt{6})^{5,2}\\\\\Rightarrow (5-2\sqrt{6})^{5,2}=(5+2\sqrt{6})^{-5,2}$