Solve Y=aX^b

$$Y = a X ^ { b }$$

Solve for X (complex solution)

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

Solve for Y

$$Y=aX^{b}$$

$$\left(X<0\text{ and }Denominator(b)\text{bmod}2=1\right)\text{ or }\left(X=0\text{ and }b>0\right)\text{ or }X>0$$