How can we simplify $\omega^{\omega\times \omega}$?

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I am trying to understand the ordinal $\omega^{\omega\times \omega}$, can it be simplified?

I come across this ordinal number as the fixed point of the normal function $\alpha\mapsto \alpha^\omega$ according to the construction on https://alchetron.com/Fixed-point-lemma-for-normal-functions . But I had a hard time understanding why intuitively it holds.