When dividing exponents with like bases you subtract the exponents.
Also, when you have like bases you divide the coefficients, and subtract the exponents.
Dividing negative exponents
Dividing uses the same rules whether the exponents are positive or negative. If you are multiplying like bases then add the exponents. If you are dividing you subtract the exponents. Use your signed number rules for adding and subtracting, and remember to always write your final answer with positive exponents.
If you end up with a negative exponent you flip it to the opposite side of the fraction in order to create the reciprocal of the negative exponent. I always teach that if the negative exponent is downstairs you move it upstairs, and if the negative exponent is upstairs you move it downstairs.
Move the x^3 to the denominator (downstairs)
With parenthesis the exponent applies to
the coefficient and variable.
In the example above: The x^-3 moves downstairs, and the (2y)^-4 moves upstairs. Remember with parenthesis the exponent applies to the coefficient and variable.
Dividing exponents with different bases
You cannot combine exponents if the bases are different
Divide the coefficients, and subtract the exponents.
Apply the rules for exponents: Subtract the exponents, and divide the coefficients.
Using the rules for exponents you subtract the exponents and divide the coefficients. After subtracting exponents, if you have a negative exponent, flip the exponent in order to create a reciprocal of the negative exponent.