Exercise 5, § 1

Show that the only triples $(m, n, p)$ of natural numbers $\neq 0$ such that $(m^n)^p = m^{np}$ are: $(1, n, p)$, $n$ and $p$ being arbitrary; $(m, n, 1)$, $m$ and $n$ arbitrary and $(m, 2, 2)$ where $m$ is arbitrary.