Solution
= Solution
The series can be written as
$$
\sum_{n=0}^\infty a_n(z^k)^n.
$$
The original power series converges when $|z|^k<2$ and diverges when $|z|^k>2$. Hence its radius as a power series in $z$ is
$$
\boxed{2^{1/k}}.
$$
= Solution
The series can be written as
$$
\sum_{n=0}^\infty a_n(z^k)^n.
$$
The original power series converges when $|z|^k<2$ and diverges when $|z|^k>2$. Hence its radius as a power series in $z$ is
$$
\boxed{2^{1/k}}.
$$