Exponentiation of a modulo sum

Question

Suppose a finite field in $F_p$, $p$ being a large prime and $g$ a generator of the field. Let two parts $A$ and $B$,with $A$ knowing a secret $a \in F_p$ and $B$ knowing another secret $b \in F_p$. Both of them want to compute: $$g^{ (a+b)\mod p} \mod p$$ without revealing their secret. Is this possible?