Prove that if $p$ is a prime and $p|k^n$, then $p^n|k^n$

Question

I want to prove that if $p$ is a prime and $p|k^n$, then $p^n|k^n$ but I have no idea where to start.

Answer 1

Hint
Show that $p|k^n \Rightarrow p|k$ using the uniqueness of prime factorisation for $k$ or, conversely that any prime factor of $k^n$ must have a multiple of $n$ as it's power.

Answer 2

The exponents of the factorization of $k^n$ are multiple of $n$. Since the exponent of $p$ in that factorization is at least $1$, it must be at least $n$.