Let $n$ be a natural number. Denote by $\omega(n)$ the number of prime divisors of $n$, and denote by $\Omega(n)$ the number of prime-power divisors of $n$.

If $n=p_1^{e_1}\cdots p_r^{e_r}$ is the factorization of $n$, then $\omega(n)=r$ and $\Omega(n)=e_1+\cdots + e_r$.

Which of the following statements are true? Select **ALL** that apply.