[Maxima-bugs] [maxima:bugs] #5710 ((-2)^(1/6))^2 simplifies to the real root (-2)^(1/3) with radexpand : false

[David S. <tom...@us...>]

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**[bugs:#5710] \(\(-2\)^\(1/6\)\)^2 simplifies to the real root \(-2\)^\(1/3\) with radexpand : false**

**Status:** open
**Group:** None
**Labels:** simplification simpexpt radexpand 
**Created:** Sat Oct 24, 2026 10:31 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:31 AM UTC
**Owner:** nobody


By Claude:

With the default `domain : real`, `(-2)^(1/3)` is the real root `-2^(1/3)`, while `(-2)^(1/6)` is the principal value `2^(1/6)*(-1)^(1/6)`. With `radexpand : false`, squaring `(-2)^(1/6)` gives `(-2)^(1/3)`, so the principal value becomes the real root, and a real root times a principal value is simplified as if both were principal values:

```
(%i1) radexpand : false$
(%i2) ((-2)^(1/6))^2;
(%o2) (-2)^(1/3)
(%i3) csign(%);
(%o3) neg
(%i4) (-2)^(1/3)*(-2)^(1/6);
(%o4) sqrt(-2)
```

With `radexpand : true`, both are right:

```
(%i5) radexpand : true$
(%i6) ((-2)^(1/6))^2;
(%o6) 2^(1/3)*((sqrt(3)*%i)/2+1/2)
(%i7) (-2)^(1/3)*(-2)^(1/6);
(%o7) -(-1)^(1/6)*sqrt(2)
```

The same happened for `(-1)^(1/6)` in bug #5705.


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