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

$\Huge { \color{#D61F06}{a} }^{ \sqrt { \log _{ \color{#D61F06}{a} }{ \color{#3D99F6}{b} } } }-{ \color{#3D99F6}{b} }^{ \sqrt { \log _{ \color{#3D99F6}{b} }{ \color{#D61F06}{a}} } }= \ ?$

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