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

*To*: mathgroup at smc.vnet.net*Subject*: [mg69160] Re: Is -1^(2/5) really undefined in R?*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 31 Aug 2006 04:39:30 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <ed0uvq$po$1@smc.vnet.net> <ed3qqi$roj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Jean-Marc Gulliet wrote: > Ben wrote: >> Is -1^(2/5) really undefined in R? > > Yes. Oops! Silly mistype of mine! Of course the line above should have read "No" rather than "Yes". I apologize for any head-scratching... Jean-Marc > >> 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 >