IMC 2002 — Keystage 3 (IWYMIC) — team Question 1

Let $m,n,p$ be real numbers. If $a=x^{m+n}y^p$, $b=x^{n+p}y^m$, $c=x^{p+m}y^n$, find $a^{m-n}b^{n-p}c^{p-m}$.