What does $2^π$ : the multiplication of $2 \pi$ many times? This is rather an intuitive question, in the sense that indeed a real number raised to the power of an irrational doesn't make sense but I wanted to know what does it mean intuitively. If $2^7=2*2*2*2*2*2*2, 2^{\frac{1}{2}}=\frac{1}{\sqrt{2}}$ and $a^b=a*a*a*a*a*...*a\, \,  b$ many times, I'm curious as to what does $2^π$ mean. Obviously it's equal to $8.8249778271...$ but what's the meaning in the aforementioned scenario?

$a^{k}$ is $a*a*...*a$, k times.
$a^{1/n}$ is the n-th root of $a$.
If $r$ is irrational, then $a^r=\lim\limits_{x \to r}a^x=\lim\limits_{k/n \to r} a^{k/n}$.
