Equation help needed urgently!?

Question

Well, it is pretty hard to type here. I'll put it in words. Hope you get it.

Left hand side (LHS) of the equation:
x to the power √x³ to the power ³√x

Right Hand Side (RHS) of the equation:
(x√x)^(x)


Now, find the sum of the positive roots of the equation.

Answer 1

Certainly, x = 0 and x = 1 will work
Hard to imagine there will be any other positive roots, but that's a guess.
If you simplify both sides using the rule (x^a)^b = x^(ab) you will end up (after a bit of simplifying) with x^x =1.
Thus my guess is correct, only 0 and 1 will work.
So: the sum of the roots I could find = 1