# Domain of ( f ( x ) ) </mrow> a </msup> wher

Domain of ${\left(f\left(x\right)\right)}^{a}$ where a is an irrational number.
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Allison Pena
When we write $f\left(x{\right)}^{a}$ we mean the following expression:
$f\left(x{\right)}^{a}={e}^{a\mathrm{ln}\left(f\left(x\right)\right)}$
which requires $f\left(x\right)$ to be positive:
Otherwise, because if we have $f\left(x\right)=-1$ then we will have for example :
$\left(-1{\right)}^{1/2},\left(-1{\right)}^{\sqrt{2}},\left(-1{\right)}^{\pi }$they are all of them not defined in $\mathbb{R}$, and the same goes for negative numbers other then $-1$