Answer
$-2$
Work Step by Step
Given : $(5x^{y})^{2}$ = $25x^{-4}$
(The empty square box is represented as y)
This implies : $5^{2}x^{2y}$ = $25x^{-4}$
(since $(ab)^{n}=a^{n}b^{n}$ and $(a^{m})^{n}=a^{mn}$)
Thus, $25$ X $x^{2y}$ = $25$ X $x^{-4}$
(since $5^{2} = 25$)
Hence, $x^{2y}=x^{-4}$
This implies : $2y=-4$
Hence, $y=\frac{-4}{2}=-2$
Final result : The value in the blank is $-2$
