In a group, what is the definition of $g^{-n}$? Sorry for the short question, I would just like to check something. My book asks to prove $(g^{n})^{-1}=g^{-n}$, but $g^{-n}$ is never defined. My guess is that the definition of $g^{-n}$ is $(g^{-1})^{n}$. Am I correct?

Yes you're correct $g^{-n}$ usually denotes $$\underbrace{g^{-1}\cdots g^{-1}}_{n \text{ times}}.$$
