From Wikipedia on Ordinal arithmetic:
The Cantor normal form also allows us to compute sums and products of ordinals: to compute the sum, for example, one need merely know that $$\omega^{\beta} c+\omega^{\beta'} c' = \omega^{\beta'}c' \,,$$ if $\beta'>\beta$ […]
Is this trivial? Can someone explain it? I don't see it yet.