You have a physical equation that needs temperature in Kelvin to some power n and you want to convert this equation to one in Celcius or even Fahrenheit for ease of computation. You might do the following.
y= (T[K])^n = (T[^oC] - 273.15[^oC] )^n
Which for n=1 is the definition of C in terms of K.
However, Mathematica gives a wrong result.
Table[UnitConvert[Quantity[1., "DegreesCelsius"]^n]^(1/n), {n, 1, 2}]
(* {274.15K,1.K} *)
0[^oC]^2 = 0[K]^2 for Mathematica, even though, 0[^oC] = 273.15[K] !
It appears Mathematica handles bad power of non-SI units that require an offset to be scaled to SI units.