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Re: Cube root of -1 and 1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90891] Re: Cube root of -1 and 1
  • From: Steven Siew <stevensiew2 at gmail.com>
  • Date: Mon, 28 Jul 2008 07:53:23 -0400 (EDT)
  • References: <g6h5fm$h26$1@smc.vnet.net>

On Jul 27, 4:44 pm, Bob F <deepyog... at gmail.com> wrote:
> Could someone explain why Mathematica evaluates these so differently?
>
Try this

Table[(Sqrt[36]-n)^(1/3),{n,0,7}]

(1)^(1/3)

(0)^(1/3)

The short answer is :

One to the power of anything is one

Zero to the power of anything (non-zero) is zero.

Zero to the power of zero is Indeterminate.

Steven Siew

> In[53]:=
>
> (Sqrt[36] - 7)^(1/3)
> (Sqrt[36] - 5)^(1/3)
>
> Out[53]= (-1)^(1/3)
>
> Out[54]= 1
>
> In other words why isn't (-1)^1/3 expressed as -1 ??
>
> Thanks...
>
> -Bob



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