Integer Power C++ Function with base and exponent parameters
Use the standard library
If you are going to give the result as a double, then this function isn't really a pure integer power calculator. And in that case, just use std::pow(). It has overloads for integer exponents that the compiler can optimize for.
A pure integer power function
If you just want to work purely on integers, then the typical algorithm to calculate a number raised to an arbitrary power efficiently is by recognizing that, for example, \$x^4 = ((x * x) * (x * x))\$, and so you can calculate \$y = x * x\$, and then \$x^4 = y * y\$. This only needs two multiplications instead of 3. So basically, you can divide and conquer the problem:
int integerPower(int base, int exponent) {
    if (exponent == 0)
        return 1;

    int result = integerPower(base, exponent / 2);
    int result *= result;

    if (exponent &amp; 1)
            result *= base;

    return result;
}    

The above doesn't work for negative exponents, but then again that is not very useful if the result is just an integer.