10. a) Show that if $a$ and $b$ are positive integers with $(a, b)=1$, then $\left(a^{n}, b^{n}\right)=1$ for all positive integers $n$.
b) Use part (a) to prove that if $a$ and $b$ are integers such that $a^{n} \mid b^{n}$ where $n$ is a positive integer, then $a \mid b$.