Solve g*y=x^sqrt{pi}

$$g \cdot y = x ^ { \sqrt { \pi } }$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{x^{\sqrt{\pi }}}{y}\text{, }&y\neq 0\\g\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yg=x^{\sqrt{\pi }}$$

Divide both sides by y.

$$\frac{yg}{y}=\frac{x^{\sqrt{\pi }}}{y}$$

Dividing by y undoes the multiplication by y.

$$g=\frac{x^{\sqrt{\pi }}}{y}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{x^{\sqrt{\pi }}}{y}\text{, }&y\neq 0\text{ and }x\geq 0\\g\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yg=x^{\sqrt{\pi }}$$

Divide both sides by y.

$$\frac{yg}{y}=\frac{x^{\sqrt{\pi }}}{y}$$

Dividing by y undoes the multiplication by y.

$$g=\frac{x^{\sqrt{\pi }}}{y}$$

Solve for x (complex solution)

$$x=\left(|g||y|\right)^{\frac{1}{\sqrt{\pi }}}e^{\frac{iarg(gy)}{\sqrt{\pi }}-2n_{1}i\sqrt{\pi }}$$

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

Solve for x

$$x=\left(gy\right)^{\frac{1}{\sqrt{\pi }}}$$

$$y=0\text{ or }g=0\text{ or }\left(\left(gy\right)^{\frac{1}{\sqrt{\pi }}}>0\text{ and }g<0\text{ and }y<0\text{ and }gy\geq 0\right)\text{ or }\left(\left(gy\right)^{\frac{1}{\sqrt{\pi }}}>0\text{ and }g>0\text{ and }y>0\text{ and }gy\geq 0\right)$$