Final answer:
The division of -12x^y by 3x^y results in -4xy, with the coefficients divided and the variables 'x^y' canceling out.
Step-by-step explanation:
The result of dividing -12x^y by 3x^y can be found by simplifying the expression. To divide terms with the same base, you subtract the exponents. However, in this case, the exponents are part of the variable representation ('x^y'), which means we treat each 'x^y' as a single term, not as x raised to the power of y. The exponents don't subtract from each other because there's no actual numeric exponent to work with. Instead, we simply divide the coefficients and since the variables and their exponents are identical, they will cancel each other out.
The coefficient -12 divided by 3 is -4, and since the variables 'x^y' are the same, we just write it once. Therefore, the answer is:
-4xy which is not listed in the provided options, assuming there's a typo and the question actually asks for the division of -12x^y by 3x^y.