Question 36694
sqrtx/sqrty=sqrt(x/y), so we can simplify the problem as sqrt(32x^5y^2/2x^3y^3), so we get sqrt(16x^2/y) = 4*(absolute value of x)/sqrty.  But x must be non-negative because 32x^5y^2 is non-negative, so we get 4x/sqrt(y).
Your method of splitting each term works also, it's just a bit longer and more confusing.