I have:

$\displaystyle \phi:X \rightarrow Y$ is a surjective homomorphism of groups.

$\displaystyle x, \bar{x} \in X$

How do I verify this statement:

If $\displaystyle x $ and $\displaystyle \bar{x}$ commute, then so do $\displaystyle x^\phi$ and $\displaystyle \bar{x}^\phi$