Commutator in hyperalgebras....

If I need to calculate some bracket like $[x_\beta^{(n)}, x_\alpha^{(m)}]$, how should I proceed? Can I proceed doing the calculation to $[x_\beta^{n}, x_\alpha^{m}]$ , then I multiply by $\frac{1}{n!m!}$ and try to write the result in a divided power notation???

Thanks.

I meant: Let $g$ be a finite-dimensional simple Lie algebra, $\{\alpha_i,...,\alpha_n\}$ the set of positive roots. Take $U_F(g\otimes C[t,t^{-1}])$ the hyperalgebra associated to $g\otimes C[t,t^{-1}]$ over some field of positive characteristic. It is well-known that there exist an integral form for $U_F(g)$ and it is generated by $(x_{\alpha,r}^-)^{(k)}$ where $k>0$, $r\in Z$ and $\alpha$ is a positive root. So, how to calculate $[ (x_{\alpha,r}^-)^{(k)}, (x_{\beta,s}^-)^{(m)}]$ ???? Is it clear now?