Taylor series expansion $ (1-\varepsilon)^{-(\kappa-1)/\kappa}$

Question

Can please someone help with finding the Taylor series expansion to this exponential? I am only looking for the first two terms, thanks!

$(1-\varepsilon)^{-(\kappa-1)/\kappa}$

Answer 1

For a constant $C$ and small $\varepsilon$, $$(1-\varepsilon)^C\approx 1-C\varepsilon+\frac {C(C-1)}2\varepsilon^2+...$$ Just plug in $$C=-\frac{\kappa-1}\kappa$$