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How can I help Mma to recognize that w can be factored out of (a w)^a (w - a w)^(1 - a). Assumptions: w>0 and 1>a>0.

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  • $\begingroup$ FullSimplify[ExpandAll[(a w)^a (w - a w)^(1 - a)] , {w > 0 , 1 > a > 0}] gets the w outside. $\endgroup$
    – Coolwater
    Jul 19 '15 at 14:22
  • $\begingroup$ @Coolwater Thanks. I had tried this with PowerExpand instead of ExpandAll, and that did not work. $\endgroup$
    – Alan
    Jul 19 '15 at 15:49
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Assuming[w > 0 && 1 > a > 0, 
 Collect[(a w)^a (w - a w)^(1 - a), w, Simplify]]

$\ $ (1 - a)^(1 - a) a^a w


Simplify[Cancel[(a w)^a (w - a w)^(1 - a)], Assumptions -> w > 0 && 1 > a > 0]

$\ $ -(-1 + a) (a/(1 - a))^a w

Simplify[Together[(a w)^a (w - a w)^(1 - a)], Assumptions -> w > 0 && 1 > a > 0]

$\ $ -(-1 + a) (a/(1 - a))^a w

Simplify[Factor[(a w)^a (w - a w)^(1 - a)], Assumptions -> w > 0 && 1 > a > 0]

$\ $ -(-1 + a) (a/(1 - a))^a w

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