Solve y=1/2x^alphaquada=

$$y = \frac { 1 } { 2 } x ^ { \alpha } \quad a =$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2y}{x^{\alpha }}\text{, }&\alpha =0\text{ or }x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\text{ and }\alpha \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}x^{\alpha }a=y$$

The equation is in standard form.

$$\frac{x^{\alpha }}{2}a=y$$

Divide both sides by \frac{1}{2}x^{\alpha }.

$$\frac{2\times \frac{x^{\alpha }}{2}a}{x^{\alpha }}=\frac{2y}{x^{\alpha }}$$

Dividing by \frac{1}{2}x^{\alpha } undoes the multiplication by \frac{1}{2}x^{\alpha }.

$$a=\frac{2y}{x^{\alpha }}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2y}{x^{\alpha }}\text{, }&x>0\text{ or }\left(Denominator(\alpha )\text{bmod}2=1\text{ and }x<0\right)\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\text{ and }\alpha >0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}x^{\alpha }a=y$$

The equation is in standard form.

$$\frac{x^{\alpha }}{2}a=y$$

Divide both sides by \frac{1}{2}x^{\alpha }.

$$\frac{2\times \frac{x^{\alpha }}{2}a}{x^{\alpha }}=\frac{2y}{x^{\alpha }}$$

Dividing by \frac{1}{2}x^{\alpha } undoes the multiplication by \frac{1}{2}x^{\alpha }.

$$a=\frac{2y}{x^{\alpha }}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=e^{-\frac{2\pi n_{1}iRe(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}-\frac{2\pi n_{1}Im(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}+\frac{arg(\frac{y}{a})Im(\alpha )+iarg(\frac{y}{a})Re(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\times \left(\frac{2|y|}{|a|}\right)^{\frac{Re(\alpha )-iIm(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\text{, }n_{1}\in \mathrm{Z}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$