Let $\Phi_n(x)$ be the nth cyclotomic polynomial over $\mathbb Q$. $\Phi_n(x)=\frac{x^n-1}{\Pi_{d|n,d<n}\Phi_d(x)}$ for n>1, and $\Phi_1(x)=x-1$
Let $n=p_1^{r_1}...p_s^{r_s}$ with $p_i$ distinct numbers and $r_i>0$. Show that $\Phi_n(x)=\Phi_{p_1...p_s}(x^{p_1^{r_1-1}...p_s^{r_s-1}})$
I don't know how to do this problem, and I am not supposed to use the Mobius inversion formula. Any help is appreciated! Thanks