# can I expand non-integer powers

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.

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

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