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.