C, 609 characters
(625 including formatted as below to avoid horizontal scrolling, 42 lines if I make it readable.)
double x(char*e,int*p);
D(char c){return c>=48&&c<=57;}
S(char c){return c==43||c==45;}
double h(char*e,int*p){double r=0,s=1,f=0,m=1;int P=*p;if(e[P]==40){
P++;r=x(e,&P);P++;}else if(D(e[P])||S(e[P])){s=S(e[P])?44-e[P++]:s;
while(D(e[P]))r=r*10+e[P++]-48;if(e[P]==46)while(D(e[++P])){f=f*10+e[P]-48;
m*=10;}r=s*(r+f/m);}*p=P;return r;}
double x(char*e,int*p){double r=0,t,d,x,s=1;do{char o=42;t=1;do{d=h(e,p);
while(e[*p]==94){(*p)++;x=h(e,p);d=pow(d,x);}t=o==42?t*d:t/d;o=e[*p];
if(o==42||o==47)(*p)++;else o=0;}while(o);r+=s*t;s=S(e[*p])?44-e[(*p)++]:0;
}while(s);return r;}
double X(char*e){int p=0;return x(e,&p);}
It's my first code golf.
I'm parsing floats myself and the only library function I use is pow.
I corrected errors with multiple elevations to a power and handling of parentheses. I also made the main function X() that takes just a string as argument. It still returns a double, though.
Expanded
42 non-blank lines
double x(char*e, int*p);
D(char c) { return c>=48 && c<=57; }
S(char c) { return c==43 || c==45; }
double h(char*e, int*p) {
double r=0, s=1, f=0, m=1;
int P=*p;
if(e[P]==40) {
P++;
r=x(e, &P);
P++; }
else if(D(e[P]) || S(e[P])) {
s=S(e[P]) ? 44-e[P++] : s;
while(D(e[P]))
r=r*10+e[P++]-48;
if(e[P]==46)
while(D(e[++P])) {
f=f*10+e[P]-48;
m*=10; }
r=s*(r+f/m); }
*p=P;
return r; }
double x(char*e, int*p) {
double r=0, t, d, x, s=1;
do {
char o=42;
t=1;
do {
d=h(e, p);
while(e[*p]==94) {
(*p)++;
x=h(e, p);
d=pow(d, x); }
t=o==42 ? t*d : t/d;
o=e[*p];
if(o==42 || o==47) (*p)++;
else o=0;
} while(o);
r+=s*t;
s=S(e[*p]) ? 44-e[(*p)++] : 0;
} while(s);
return r; }
double X(char*e) {int p=0; return x(e, &p);}
