Given $g$, $b$, $g^{ab}$, is finding $g^a$ a hard problem? As in the title, given $g$, $g^{ab}$ are big elements in a prime group $Z_p$ and $b$ in prime group $Z_r$ ($p &gt; r$, $g$ is one generator of $Z_p$). $a$ is unknown and also in $Z_r$, is finding $g^a$ a hard problem?

update $a$, $b$ and $ab$ are group elements of $Z_r$..
Not at all. It's very trivial:
$$(g^{ab})^{b^{-1}}=g^a$$