If you're multiplying 2 numbers that are the same, and they each have an exponent, how do you determine what the new exponent will be?

If the bases are the same, then u keep the same base and add the exponents

examples :
2^3 * 2^4 = 2^(3 + 4) = 2^7
3^3 * 3^3 = 3^(3 + 3) = 3^6

this does not apply if u have different bases
if u have different bases, u have to work them out..
examples :
2^2 * 3^2 = 4 * 9 = 36
3^3 * 2^2 = 27 * 4 = 108