$A=\bigg(-2\dfrac{1}{2}x^2yz^2\bigg)^3.(-2xyz)^2$
$=\bigg(-\dfrac{5}{2}x^2yz^2\bigg)^3.(-2)^2x^2y^2z^2$
$=\bigg(-\dfrac{5}{2}\bigg)^3(x^2)^3y^3(z^2)^3.4x^2y^2z^2$
$=-\dfrac{125}{8}x^6y^3z^6.4x^2y^2z^2$
$=\bigg(-\dfrac{125}{8}.4\bigg)(x^6.x^2)(y^3.y^2)(z^6.z^2)$
$=-\dfrac{125}{2}x^8y^5z^8$