Let $\sum_0^{\infty} a_n z^n$ have radius of convergence $R$ with $0< R< \infty$. Let $\alpha>0$. Find the radius of convergence of $\sum_0^{\infty} |a_n|^{\alpha} z^n$.
I tried to start with what I am given: so the series $\sum_0^{\infty} a_n z^n$ converges uniformly and absolutely for every $|z| Is this a good start: Say I take some $r$ such that $|z|