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Re: Is -1^(2/5) really undefined in R?

• To: mathgroup at smc.vnet.net
• Subject: [mg69102] Re: Is -1^(2/5) really undefined in R?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 30 Aug 2006 06:33:05 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <ed0uvq$po$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Ben wrote:
> Is -1^(2/5) really undefined in R?

Yes.

> Mathematica seems to think so, I guess since it looks like a negative square root, but
> 
> -1^(2/5) = (-1^2)^(1/5) = 1^(1/5) = 1
> 
> Is this correct mathematically?

No. See "College Algebra Tutorial 5: Rational Exponents" at 
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut5_ratexp.htm

In[12]:=
((-1)^(1/5))^2

Out[12]=
     2/5
(-1)

In[13]:=
(-1)^(2/5)==((-1)^(1/5))^2

Out[13]=
True

(-1)^(2/5)==((-1)^2)^(1/5)

Out[14]=
False

HTH,
Jean-Marc