About Cardinal Exponentiation

Question

I know the definition of a cardinal to the power of another cardinal:

$|A|^{|B|}=|$the set of all functions from $B$ to $A|$

I also know that $2^{|A|}=|\mathscr{P}(A)|$. My question is:

Is there a more generalized, simple answer for any integer to the power of a cardinal? Like $3^{|A|}?$

Answer 1

As @BrianM.Scott commented, for an integer $n\ge2$ and an infinite set $A$, $n^{|A|}=2^{|A|}=|\mathscr{P}(A)|$.