  In 1982, J\'onsson and McKenzie posed the following problem: "Find counter
examples (or prove that none exist) to the refinement of $A^C\cong B^D$ [$A$,
$B$, $C$, and $D$ non-empty posets] under" the condition "$C$, $D$, and $A^C$
are finite and connected." That is, in this situation, are there posets $E$,
$X$, $Y$, and $Z$ such that $A\cong E^X$, $B\cong E^Y$, $C\cong Y\times Z$, and
$D\cong X\times Z$?
  In this note, this problem is solved.
