Can a factorial have an exponent

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can you do $(4!)^4$ or do you have to do $4! \times 4$, I have looked on google but can't find anything to prove or disprove if it's possible.

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I'm not sure I understand your question, but here is a shot at it:

$4!$ is just a number -- specifically, it's the number $24$. So $(4!)^4$ is exactly the same thing as $24^4$, which is $331,776$.