(2x^2)^(3/2)/(2^(1/2))*x^4
Assuming the usual carelessness with parentheses, I'll interpret your expression as
(2x^2)^(3/2)/((2^(1/2))*x^4)
(2x^2)^(3/2) = 2^(3/2) * x^3
So, you have
2^(3/2) x^3
---------------- = 2/x
2^(1/2) x^4
(2x^2)^(3/2)/((2^(1/2))*x^4)
(2x^2)^(3/2) = 2^(3/2) * x^3
So, you have
2^(3/2) x^3
---------------- = 2/x
2^(1/2) x^4