Sure. Just do it...
(x^4 - 1)^(1/3) = (x^4)^{1/3} + (1/3)
It is a wonderfully useful result.
It is only a minor generalization from the finite Binomial Expansion
See how it starts out with the first tern to the external exponent?
Then we start reducing the exponent on the first term and increasing the exponent on the second term. The rest is just controlling the combinations.