For an integer number $a$

$$x^a=\{(x)(x)(x)...(x)\} (a\,times)$$ $$x^{\frac{1}{b}}=n\rightarrow\;\{(n)(n)(n)...(n)\}(b\,times)=x$$

For rational number $m=\frac{a}{b}$

$$x^m=x^\frac{a}{b}=(x^a)^\frac{1}{b}$$

And can be though of as a combination of the situations before

What about

$$x^e$$

How would one calculate or picture this from more basic operations?