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sage: var("q,n,k,x", domain="positive")
(q, n, k, x)
sage: (((q - 1)*x + 1)^n*q^n - ((q^2 - q)*x + q)^n).canonicalize_radical()

The canonicalize_radical method is often relevant for symbolic expressions involving powers or radicals. Note however that this method may not be always legitimate (see its docs...).