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
>
> 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
>

```

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