So first 81^-3/4 is cubing 81, finding the forth root, and then putting it on the denominator. Doing this you get 1/27.
Now you think, how do I get 3 to equal 27?
3^1 = 3
3^2 = 9
3^3 = 27
From here you just put a negative in front of the power, 3^-3, which puts the 27 on the bottom of the fraction, leaving you with 1/27, which is what we were trying to get.
