       Re: simple Simplify[] question

• To: mathgroup at smc.vnet.net
• Subject: [mg19787] Re: [mg19766] simple Simplify[] question
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Fri, 17 Sep 1999 01:36:43 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```This sort of question comes up regularly. It's nothing to do with
Mathematica really, it's just mathematics. First of all, this
"simplification" is not valid when a is a  complex numbers:
In:=
(-1 + I)^3
Out=
2 + 2 I

In:=
((-1 + I)^2)^(3/2)
Out=
-2 - 2 I

Actually, it is not even valid when a is a real negative number:

In:=
(-1)^3
Out=
-1

In:=
((-1)^2)^(3/2)
Out=
1

If you have Mathematica 4 you can do this:
In:=
Simplify[(a^2)^(3/2), a \[Element] Reals]
Out=
3
Abs[a]

or this:

In:=
Simplify[(a^2)^(3/2), a >= 0]
Out=
3
a

If not, and you are dealing with non-negative numbers perhaps the simplest
thing to do is to write Abs[a] instead of a (and if necessary later replace
Abs[a] by a) thus:

In:=
Simplify[(Abs[a]^2)^(3/2)]  /. Abs[a] -> a
Out=
3
a

--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: Ulf Saalmann <us at atom.msi.se>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19787] [mg19766] simple Simplify[] question
>Date: Wed, Sep 15, 1999, 4:53 PM
>

>
>
>  Hello,
>
>  why gives Mathematica
>                                      2 3/2
>       Simplify[(a^2)^(3/2)]        (a )
>
>
>  and not
>                                       3
>                                     a
>
>  and how to convince Mathematica to do it?
>
>
>  Thanks
>          Ulf  (us at atom.msi.se)
>

```

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