Solve =u=x^y^2

$$= u = x ^ { y ^ { 2 } }$$

Solve for x (complex solution)

$$x=e^{\frac{arg(u)Im(y^{2})+iarg(u)Re(y^{2})}{\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)^{2}}-\frac{2\pi n_{1}iRe(y^{2})}{\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)^{2}}-\frac{2\pi n_{1}Im(y^{2})}{\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)^{2}}}\left(|u|\right)^{\frac{Re(y^{2})-iIm(y^{2})}{\left(\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for u

$$u=x^{y^{2}}$$

$$\left(x<0\text{ and }Denominator(y^{2})\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }y\neq 0\right)\text{ or }x>0$$

Solve for x

$$\left\{\begin{matrix}x=u^{\frac{1}{y^{2}}}\text{, }&\left(Denominator(\frac{1}{y^{2}})\text{bmod}2=1\text{ and }y\neq 0\text{ and }Numerator(y^{2})\text{bmod}2=1\text{ and }Denominator(y^{2})\text{bmod}2=1\text{ and }u^{\frac{1}{y^{2}}}\neq 0\text{ and }u<0\right)\text{ or }\left(y\neq 0\text{ and }u\geq 0\right)\\x=-u^{\frac{1}{y^{2}}}\text{, }&\left(u^{\frac{1}{y^{2}}}<0\text{ and }y\neq 0\text{ and }u>0\text{ and }Numerator(y^{2})\text{bmod}2=0\right)\text{ or }\left(Numerator(y^{2})\text{bmod}2=0\text{ and }y\neq 0\text{ and }u=0\right)\text{ or }\left(y\neq 0\text{ and }u>0\text{ and }Numerator(y^{2})\text{bmod}2=0\text{ and }Denominator(y^{2})\text{bmod}2=1\right)\text{ or }\left(Denominator(\frac{1}{y^{2}})\text{bmod}2=1\text{ and }y\neq 0\text{ and }Numerator(y^{2})\text{bmod}2=0\text{ and }Numerator(y^{2})\text{bmod}2=1\text{ and }Denominator(y^{2})\text{bmod}2=1\text{ and }u^{\frac{1}{y^{2}}}\neq 0\text{ and }u<0\right)\\x\neq 0\text{, }&y=0\text{ and }u=1\end{matrix}\right.$$