## Algebra 1

$-2$
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 $-2$