how would you solve for y in this problem:

x=(y^2+3y)^(1/3)

would it equal: y= x^3/y - 3 ?

and what about this problem:
x= 1/[(y^2+3y-5)^3]

would it equal: y = y/x + 5/y - 3?

I would appreciate your help very much!

<<how would you solve for y in this problem:
x=(y^2+3y)^(1/3)

would it equal: y= x^3/y - 3 ? >>

Your equation is correct but it does not allow you to solve explicitly for y. What you have to do is treat the "x-containing" term as if it were a constant in the quadratic equation:

y^2 + 3y -x^3 = 0

Then use the equation for the root of quadratic equations:
y = [-6 +/- sqrt (9 + 4x^3)]/2

The second question can be handled similarly.