Recursive Power Function Complexity

What is the time complexity of the following recursive power method with respect to the parameter exp?

public int power(int base, int exp) {
    if(exp == 0) return 1;
    int half = power(base, exp / 2);
    if(exp % 2 == 0) {
        return half * half;
    } else {
        return base * half * half;
    }
}