what does (1+cube root of x)^2 equal

(1 + 2 x^1/3  + x^2/3) 

This is as

$$1+2\sqrt[3]x+\sqrt[3]{x^2}\\\\
OR\\\\
1+2\sqrt[3]x+\left(\sqrt[3]x\right)^2\\\\$$

OK....so we have......

(1 + x^1/3)² =

(1 + x^1/3) * (1 + x^1/3)   =

(1 + 2 x^1/3  + x^2/3)     ....... remember, by the laws of exponents,  aⁿ * aⁿ = a²ⁿ....so x^1/3 * x^1/3 = x^2/3  !!!