Question 95673
(x^2y^-3z)^1/2
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x^1/2yz^-1/2 

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= [x y^(-3/2)z^(1/2)] / [x^(1/2) y z^(-1/2)]

Look at the x factors: x^1/x^(1/2) = x^(1/2)
Look at the y factors: y^(-3/2)/y^1 = 1/y(5/2)
Look at the z factors: z^(1/2)/z^(-1/2) = z
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Result; [x^(1/2)z]/[y^(5/2)]