\(\cos^{-1}x\) could be used to denote the inverse cosine function, while \((\cos x)^{-1}\) probably instead refers to the reciprocal cosine function, i.e. the secant function.
In general, \(\cos^{-1}x
eq(\cos x)^{-1}\), but it's not unheard of for them to mean the same thing, especially in a context where something like \(\arccos x\) is used explicitly to denote the inverse function. I'd be careful about assuming they are always the same.
