Question

Помогите с алгеброй! 10 класс, корни)

Answer 1

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

Answer 2

$((5*5 {}^{ \frac{1}{2} } ) {}^{ - \frac{2}{3} } + \sqrt[4]{81} {}^{ - 1} )*((5*5 {}^{ \frac{1}{2} } ) {}^{ - \frac{2}{3} } - \frac{1}{81 {}^{ \frac{1}{4} } } ) = \\ \\ ((5 {}^{ \frac{3}{2} } ) {}^{ - \frac{2}{3} } + 3 {}^{ - 1} )*((5 {}^{ \frac{3}{2} } ) {}^{ - \frac{2}{3} } - \frac{1}{(3 {}^{4}) } {}^{ \frac{1}{4} } ) = \\ \\ (5 {}^{ - 1} + \frac{1}{3} )*(5 {}^{ - 1} - \frac{1}{3} ) = \\ \\ ( \frac{1}{5} + \frac{1}{3} )*( \frac{1}{5} - \frac{1}{3} ) = \\ \\ \frac{8}{15} *( - \frac{2}{15} ) = \\ \\ - \frac{16}{225}$