Question

Записать в виде рационального числа:

Answer 1

$[(5\sqrt{5})^{-\frac{2}{3}} +\sqrt[4]{81^{-1}} ]*[(5\sqrt{5})^{-\frac{2}{3}} -81^{-\frac{1}{4}}]=[(5\sqrt{5})^{-\frac{2}{3}} +81^{-\frac{1}{4}}} ]*[(5\sqrt{5})^{-\frac{2}{3}} -81^{-\frac{1}{4}}]=\\\\=[(5\sqrt{5})-^{\frac{2}{3}}]^{2}-(81^{-\frac{1}{4}})^{2}=(5\sqrt{5})^{-\frac{4}{3}}-81 ^{-\frac{1}{2}} =(5^{\frac{3}{2}})^{-\frac{4}{3}}-(9^{2})^{-\frac{1}{2}}=5^{-2}-9^{-1}=\\\\=\frac{1}{25}-\frac{1}{9}=\frac{9-25}{25*9}=-\frac{16}{225}$