For \( a, b \in \mathbb{R}^+ \) and \( >1 \),

\[ \Huge { \color{red}{a} }^{ \sqrt { \log _{ \color{red}{a} }{ \color{blue}{b} } } }-{ \color{blue}{b} }^{ \sqrt { \log _{ \color{blue}{b} }{ \color{red}{a}} } }= \ ? \]

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