(2 - Sqrt[2] 3^(1/4))^(1/4)/(-1 + Sqrt[3])^(7/12) = = (23 - 12 Sqrt[2] 3^(1/4) + 13 Sqrt[3] - 7 Sqrt[2] 3^(3/4))^(1/6)/2^(1/3) but not the numerator nor denominator separately. Corey's RationalizeDenominator further simplifies to (2 - Sqrt[2] 3^(1/4))^(1/4)/(-1 + Sqrt[3])^(7/12) = = 1/(5 - Sqrt[3] + Sqrt[2] 3^(3/4))^(1/6) https://community.wolfram.com/groups/-/m/t/980264 —rwg Given the reciprocal of the above quotient, the denester prints out the 6th root of the trinomial, but then hangs up for hours.