Answer
$$-4t^4+3t^3+1$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{36t^6-27t^5-9t^2}{-9t^2}\\ -\left(4t^4-3t^3-1\right) \\ -4t^4+3t^3+1$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.
