Solve x^sqrt{y}=7/x^2y^3

$$x ^ { \sqrt { y } } = \frac { 7 } { x ^ { 2 } y ^ { 3 } }$$

Solve for x (complex solution)

$$x=7^{\frac{Re(\sqrt{y})-iIm(\sqrt{y})}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}}e^{-\frac{2\pi Re(\sqrt{y})n_{1}i}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}-\frac{2\pi Im(\sqrt{y})n_{1}}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}-\frac{4\pi n_{1}i}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}+\frac{arg(\frac{1}{y^{3}})Im(\sqrt{y})+iarg(\frac{1}{y^{3}})Re(\sqrt{y})+2iarg(\frac{1}{y^{3}})}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}}\times 49^{\frac{1}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}}\left(|y|\right)^{\frac{3\left(-Re(\sqrt{y})-2+iIm(\sqrt{y})\right)}{\sqrt{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}+4Re(\sqrt{y})+4}}$$

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

$$y\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=-\left(\frac{7}{y^{3}}\right)^{\frac{1}{\sqrt{y}+2}}\text{, }&\left(\frac{7}{y^{3}}\right)^{\frac{1}{\sqrt{y}+2}}>0\text{ and }Numerator(\sqrt{y}+2)\text{bmod}2=0\text{ and }Denominator(\sqrt{y})\text{bmod}2=1\text{ and }y>0\\x=\left(\frac{7}{y^{3}}\right)^{\frac{1}{\sqrt{y}+2}}\text{, }&\left(\frac{7}{y^{3}}\right)^{\frac{1}{\sqrt{y}+2}}>0\text{ and }y>0\end{matrix}\right.$$