Let $p$ be a prime. The Frobenius map: $x \mapsto x^3$ is bijective from $\mathbb{F}_p \longrightarrow \mathbb{F}_p$. I'm trying to write its inverse map: $x \mapsto x^{?}$. I suppose the ($?$) must be a power of $p$. Is it something like $x \mapsto x^{{p}^{p-1}}$ ?
Any help would be greatly appreciated.