The properties of exponents used to simplify the expression are:
(a^m)^n = a^(m*n)
(a^m)^n = (a^n)^m
(a*b)^n = a^n * b^n
(a/b)^n = a^n / b^n
Using these properties, we can simplify the expression as follows:
(y3/2 x -1/2)^4
= (y^3/2 * x^-1/2)^4
= y^3/2 4 * x^-1/2 4
= y^(3/24) * x^(-1/24)
= y^6 * x^-2
So the simplified expression is: y^6 * x^-2