To simplify a cross product involving vectors with coefficients, the coefficients can be factored out. For instance, in the expression (x/(y^3))\bar{r} X (x/(y))\bar{L}, the coefficients can be extracted. This follows the rule that (a\vec{u})\times(b\vec{v}) equals ab (\vec{u}\times \vec{v}). Thus, the simplification process involves multiplying the coefficients and then calculating the cross product of the unit vectors. This approach streamlines the calculation and clarifies the relationship between the vectors.