Lös z=x^2y

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

Lös ut x (complex solution)

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

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

Lös ut y (complex solution)

$$\left\{\begin{matrix}y=\frac{\pi n_{1}i}{\ln(x)}+\frac{\log_{x}\left(z\right)}{2}\text{, }n_{1}\in \mathrm{Z}\text{, }&z\neq 0\text{ and }x\neq 1\text{ and }x\neq 0\\y\in \mathrm{C}\text{, }&\left(x=0\text{ and }z=0\right)\text{ or }\left(x=1\text{ and }z=1\right)\end{matrix}\right,$$

Lös ut x

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