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.