If b is the base and we have b^x divided by b^y the quotient is b^(x-y). The way to understand this is to write:
b*b*b*...*b (x b's multiplied together) = b^x and b*b*...*b (y b's multiplied together). Now divide and we end with b's cancelling out leaving (x-y) b's or (y-x) b's in the denominator which is 1/b^(y-x)=b^-(x-y). x and y can also be fractions, which is the basis of logarithms, because we add logs when we want to add and subtract when we want to divide. So the answer is true, even when b and its exponent are just one of a set of factors in the numerator or denominator.