manipulating powers
- To: mathgroup at smc.vnet.net
- Subject: [mg57275] manipulating powers
- From: "Marc Hesse" <mhesse at stanford.edu>
- Date: Mon, 23 May 2005 02:20:43 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I have problems manipulating powers. Here are wo of my common problems.
1) Collecting terms under a power
In[1]:=f[x_, y_] := (x - b*x)^a
Collect[f[x, y], x]
Out[2]=(x - b x)^a
The only thing I can get to work is this
In[9]:=PowerExpand[Collect[PowerExpand[f[x, y]^(1/a)], x]^a]
Out[9]=(1 - b)^a x^a
but that seems very convoluted, and I hope there is an easier way, because I
need to work with large complicated expressions.
2) Splitting a sum in a power
In[14]:=(xi^(1/2) + xi^(1/2 + a^2)
where I would like to split the summ in the second exponent, and collect the
Sqrt[x].
In[15]:=Collect[%, Sqrt[xi]]
Out[15]=xi + xi^(1\/2 + a^2)
even if I substitue manulally Mathematica puts recombines the exponentials
% /. {xi^(1/2 + a^2) -> Sqrt[xi]*xi^(a^2)}
Collect[%, Sqrt[xi]]
xi + xi^(1/2 + a^2)
I hope there is a better way of doing these basic manipulations,
any hep is appreciated
Marc