       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:=f[x_, y_] := (x - b*x)^a
Collect[f[x, y], x]
Out=(x - b x)^a

The only thing I can get to work is this
In:=PowerExpand[Collect[PowerExpand[f[x, y]^(1/a)], x]^a]
Out=(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:=(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:=Collect[%, Sqrt[xi]]
Out=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

```

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