Elementary Number Theory: If $p$ and $a$ are natural numbers with prime $p$, and $p^4|a^3$, then $p^2|a$.
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.