The great log

Algebra Level 3

\[ \Large \left( \frac{81^{\frac{1}{\log_{5}9}}+3^{\frac{3}{\log_{\sqrt{6}}3}}}{409}\right) \left((\sqrt{7})^{\frac{2}{\log_{25}7}}-(125)^{\log_{25}6}\right)= \, ? \]

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