If we apply the rules of exponents that have the same base, we know to add when multiplying.
An example of this would be x^3 * x^7 = x^3+7= x^10.
In this case, even though we have a number, the same rules apply.
So 81^-1/2 times 81^3/2 = 81^-1/2+3/2 = 81^1 = 81.
A really complex way to get nowhere!