Question

Вычислите
$(5 ^{ \sqrt{5} + \sqrt{3} }) ^{ \sqrt{3} - \sqrt{5} }$
помагите пж​

Answer 1

$(5^{\sqrt{5}+\sqrt{3}})^{\sqrt{3}-\sqrt{5} = 5^{(\sqrt{5}+\sqrt{3})(\sqrt{3}-\sqrt{5})} = 5^{(\sqrt{3}+\sqrt{5})(\sqrt{3}-\sqrt{5})} = 5^{3-5}=5^{-2}=\frac{1}{25}.$