I have thought about it and see no logical way to solve it due to not seeing a relation between the m and y and n and x. if then show that xyz = 1
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This is a neat problem. From the given: $\displaystyle m^y=a^{xy}~\&~n^x=a^{xy}$ so $\displaystyle m^x\cdot n^y=a^{2xy}$ Therefore, $\displaystyle a^{2}=(m^x\cdot n^y)^z=a^{2xyz}$. You finish.
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