Simple ordinal number question

Question

I got an excercise to add some ordinals, and one of given ordinals was: $$\omega\cdot4\omega^2+1.$$ I know that $4\omega = \omega$ and that multiplication is associative, so I think this simply equals to $\omega^3+1$?

I don't feel confident about this and so I would like to hear some confirmation.

Answer 1

To get this off the unanswered list,

Yes. Your argument is correct.