polynomials - How to evaluate GF(256) element

I wonder is there any easy way to evaluate elements of GF$(256)$: meaning that I would like to know what $\alpha^{32}$ or $\alpha^{200}$ is in polynomial form? I am assuming that the primitive polynomial is $D^8+D^4+D^3+D^2+1$. For example for GF$(8)$ what we do is as follow to calculate $\alpha^3$ is divide it by $\alpha^3+\alpha+1$ and we get $\alpha+1$ but here in GF$(256)$ this will be really tedious so I would like to know is there any way to calculate above expressions or similar expressions like $\alpha^{100}$ in GF$(256)$.

Thanks.