Laurent series expansion $\exp({\frac{1}{z^4}})$

Question

I apologize in advance if this is very basic and usually I don’t have any problems with Laurent series, however I am stuck how to compute the Laurent series of $\exp( \frac{1}{z^4} )$ about $z=1$. I fail to see which algebraic manipulation would lead me to the result.

Answer 1

At $1$, it has a Taylor series with radius of convergence $1$.

I computed the first $3$ terms: $$e^{1/z^4}=e-4e(z-1)+18e(z-1)^2+O((z-1)^3).$$