If the $i^{th},j^{th}\; and\; k^{th}$ term of an AP and a GP are equal and are $x,y,z$ find the value of $x^{(y-z)}\;.y^{(z-x)}\;.z^{(x-y)}$

Question

$\begin{array}{1 1} xyz \\ \large\frac{x+y+z}{2} \\ 1 \\ (x-y)(y-z)(z-x) \end{array}$