First, let's simplify the expression inside the parentheses:
(3m^6n^3)^4 = 3^4 m^24 n^12 = 81m^24n^12

Now, let's simplify the entire expression:
(81m^24n^12) * (-1/81m^9n) = -m^15n11

So, the simplified expression is -m^15n^11.