# How do you simplify ((x^2y^-3z)^(1/2))/(x^(1/2)yz^(-1/2))?

$= \left({x}^{\frac{1}{2}} {y}^{- \frac{5}{2}} z\right)$
$= {\left({x}^{2} {y}^{-} 3 z\right)}^{\frac{1}{2}} / \left({x}^{\frac{1}{2}} y {z}^{- \frac{1}{2}}\right)$
$= \frac{{x}^{2 \times \frac{1}{2}} {y}^{- 3 \times \frac{1}{2}} {z}^{\frac{1}{2}}}{{x}^{\frac{1}{2}} y {z}^{- \frac{1}{2}}}$
$= \left(x {y}^{- \frac{3}{2}} {z}^{\frac{1}{2}} \cdot {x}^{- \frac{1}{2}} \cdot {y}^{-} 1 \cdot {z}^{\frac{1}{2}}\right)$
$= {x}^{1 - \frac{1}{2}} {y}^{- \frac{3}{2} - 1} {z}^{\frac{1}{2} + \frac{1}{2}}$
$= \left({x}^{\frac{1}{2}} {y}^{- \frac{5}{2}} z\right)$