If _10000x = - 1/4 , then the value of x is = ?

Answer: Option A

$$\begin{array}{rl}& \text{let }{\log }_{10000}x=-\frac{1}{4}\\ & \Rightarrow x={\left(10000\right)}^{-\frac{1}{4}}\\ & ={\left({10}^4\right)}^{-\frac{1}{4}}\\ & =10^{-1}\\ & =\frac{1}{10}\end{array}$$