The PR https://github.com/sagemath/sage/pull/38362 is for adding 
deprecation warning to the use of AA(x)^(1/n) to get the real root.
The PR https://github.com/sagemath/sage/pull/38564 will change the behavior 
of AA(x)^(1/n) after one year deprecation period.
Adding P(x).pow(m/n) = AA(x).nth_root(n)**m will be provided for fractional 
power computation in the parent P (including AA).

Voting for this change is going on 
https://github.com/sagemath/sage/pull/38362.

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