Euler equation guess and verify
Hint:
Note that
\begin{equation}
k_{t+1}=gk_t^a \quad\Rightarrow\quad g=\frac{k_{t+1}}{k_t^a}=\frac{k_{t+2}}{k_{t+1}^a}.
\end{equation}
Rearrange your Euler condition into a form such that you can use $g$ to sub-out the above ratios. Then it should be straightforward to solve for $g$.