F#, 589 chars
I golf-compressed my prior solution into this gem:
let rec D a=function|c::s when System.Char.IsDigit c->D(c::a)s|s->a,s
and L p o s=
let rec K(a,s)=match o s with|None->a,s|Some(o,t)->let q,t=p t in K(o a q,t)
K(p s)
and E=L(L F (function|'*'::s->Some((*),s)|'/'::s->Some((/),s)|_->None))(
function|'+'::s->Some((+),s)|'-'::s->Some((-),s)|_->None)
and F s=match P s with|x,'^'::s->let y,s=F s in x**y,s|r->r
and P=function|'('::s->let r,_::s=E s in r,s|s->(
let a,s=match(match s with|'-'::t->D['-']t|_->D[]s)with|a,'.'::t->D('.'::a)t|r->r
float(new string(Seq.to_array(List.rev a))),s)
and G s=string(fst(E(Seq.to_list s)))
Tests:
printfn "%s" (G "1.1+2.2+10^2^3") // 100000003.3
printfn "%s" (G "10+3.14/2") // 11.57
printfn "%s" (G "(10+3.14)/2") // 6.57
printfn "%s" (G "-1^(-3*4/-6)") // 1
printfn "%s" (G "-2^(2^(4-1))") // 256
printfn "%s" (G "2*6/4^2*4/3") // 1
printfn "%s" (G "3-2-1") // 0
