Answer
$10^{-4}=\frac{1}{10000}$
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{10}\frac{1}{10000}=-4$ means the same as $10^{-4}=\frac{1}{10000}$.