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)