This is presumably due to the fact that the Power function (which is what is being used in the form of the expression in the second example) is defined with a particular convention for a branch cut. From the documentation for Power:
Power[x,y] has a branch cut discontinuity for non-integer y running
from -[Infinity] to 0 in the complex x plane.
FullForm[1/((x^2 - 1)^4)^(1/5)]
gives
Power[Power[Plus[-1,Power[x,2]],4],Rational[-1,5]]
whereas
FullForm[1/(x^2 - 1)^(4/5)]
gives
Power[Plus[-1, Power[x, 2]], Rational[-4, 5]]
