  The higher order Kirchhoff type equation $$\int_{\mathbb{R}^{2m}}(|\nabla^m
u|^2 +\sum_{\gamma=0}^{m-1}a_{\gamma}(x)|\nabla^{\gamma}u|^2)dx
\left((-\Delta)^m u+\sum_{\gamma=0}^{m-1}(-1)^\gamma
\nabla^\gamma\cdot(a_\gamma (x)\nabla^\gamma u)\right)
=\frac{f(x,u)}{|x|^\beta}+\epsilon h(x)\ \ \text{in}\ \ \mathbb{R}^{2m}$$ is
considered in this paper. We assume that the nonlinearity of the equation has
exponential critical growth and prove that, for a positive $\epsilon$ which is
small enough, there are two distinct nontrivial solutions to the equation. When
$\epsilon=0$, we also prove that the equation has a nontrivial mountain-pass
type solution.
