Which expression is equivalent to (x^1/2 y^-1/4 z)^-2

We can distribute the outer exponent of -2 to each inner exponent:
x^(1/2*-2) y^(-1/4*-2) z^(-2)
This simplifies to:
x^(-1) y^(1/2) z^(-2)
Then if we express the negative exponents as fractional terms:
y^(1/2) / (xz^2)
The exponent of 1/2 can also be written as a square root:
sqrt(y) / (xz^2)