Really hard problem!!
$ \begin{align} xy&=-2 \\ xy^{a-1} &=-512 \\ x(y^a-1 ) &= 341y-341 \end{align} $
Really hard problem!!
$ \begin{align} xy&=-2 \\ xy^{a-1} &=-512 \\ x(y^a-1 ) &= 341y-341 \end{align} $
From the first two (divide them) you get $y^{a-2}=256$.
So the third becomes $xy\cdot y \cdot 256 -x=341y-341$.
$-512 y-x=341y-341$. Plug $x=-2/y$ in this last equation you get a quadratic equation.
It is not really that hard problem. You just have to play a bit with it.