       Re: Mathematica strange behaviour finding a cubic root

• To: mathgroup at smc.vnet.net
• Subject: [mg129120] Re: Mathematica strange behaviour finding a cubic root
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 17 Dec 2012 02:53:26 -0500 (EST)
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```The possibly unexpected results your seeing are because, by definition,
Mathematica gives the _principal_ roots with such fractional powers. In
particular, a power b^(m/n) with b < 0, m an even positive integer, and
n an odd positive integer will be non-real complex.

To force Mathematica to return the real cube-roots, etc., there are
several approaches. The simplest, now with Mathematica 9, is to use
Surd:

Surd[-1/2, 3]^2
2^(-2/3)

(where I'm showing the InputForm of the output).

On Dec 16, 2012, at 1:06 AM, sergio_r at mail.com wrote:

>
> How can I make Mathematica provides the same answer for
> (-1/2)^(2/3) = ((-1/2)^2)^(1/3) ?
>
> What follows is a Mathematica session:
>
> In:= (-1/2)^(2/3)
>
>           1  2/3
> Out= (-(-))
>           2
>
> In:= N[%]
>
> Out= -0.31498 + 0.545562 I
>
> In:= ((-1/2)^2)^(1/3)
>
>         -(2/3)
> Out= 2
>
> In:= N[%]
>
> Out= 0.629961
>
>
> Sergio

---
Murray Eisenberg                                    murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305

```

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