Power[__] Pattern works like Level

Question

I came across this case:

expr = {x, Cos[Exp[x]], x^a}

Cases[expr, Power[__], -1]
(*{x,E,x,E^x,Cos[E^x],x,a,x^a}*)

Level[expr, -1]
(*{x,E,x,E^x,Cos[E^x],x,a,x^a}*)

What is going on here? Why Power[__] (or Power[_] ) Works like Level?

Thanks

Answer 1

Very simply Power[__] evaluates to __ and __ matches any expression:

expr = {x, Cos[Exp[x]], x^a};

Power[__]

Cases[expr, __, -1]

__

{x, E, x, E^x, Cos[E^x], x, a, x^a}

Answer 2

_^_ instead of Power[__] may give you the result you desire. The issue is that all expressions strictly match themselves to the first power!

MatchQ[x, Power[__]]

True

MatchQ[x, Power[_, 1]]

True

MatchQ[x, _^_]

False

Considering you example...

 expr = {x, Cos[Exp[x]], x^a}

 Cases[expr, _^_, -1] // InputForm

{E^x, x^a}