Commuting 3D Rotations Special Case?

Question

I have a product of 3D rotations such as $$\prod_{i=1}^{n}R_0R_i=R_0R_1R_0R_2R_0R_3\dots$$ Note that $R_0$ is constant. I would like to rearrange the product separating the $R_0$'s from the rest such that I can compute those separately. Something like $$\prod_{i=1}^{n}R_0R_i=f(R_0,n)\cdot g(R_1, R_2, \dots)$$ Is this possible at all? Thanks in advance.