Solve e=mc^p

$$e = m c ^ { p }$$

Solve for m (complex solution)

$$m=\frac{e}{c^{p}}$$

$$p=0\text{ or }c\neq 0$$

Steps for Solving Linear Equation

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

$$mc^{p}=e$$

The equation is in standard form.

$$c^{p}m=e$$

Divide both sides by c^{p}.

$$\frac{c^{p}m}{c^{p}}=\frac{e}{c^{p}}$$

Dividing by c^{p} undoes the multiplication by c^{p}.

$$m=\frac{e}{c^{p}}$$

Solve for m

$$m=\frac{e}{c^{p}}$$

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

Steps for Solving Linear Equation

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

$$mc^{p}=e$$

The equation is in standard form.

$$c^{p}m=e$$

Divide both sides by c^{p}.

$$\frac{c^{p}m}{c^{p}}=\frac{e}{c^{p}}$$

Dividing by c^{p} undoes the multiplication by c^{p}.

$$m=\frac{e}{c^{p}}$$

Solve for c (complex solution)

$$c=e^{-\frac{2\pi n_{1}iRe(p)}{\left(Re(p)\right)^{2}+\left(Im(p)\right)^{2}}-\frac{2\pi n_{1}Im(p)}{\left(Re(p)\right)^{2}+\left(Im(p)\right)^{2}}+\frac{Re(p)-iIm(p)+arg(\frac{1}{m})Im(p)+iarg(\frac{1}{m})Re(p)}{\left(Re(p)\right)^{2}+\left(Im(p)\right)^{2}}}\left(|m|\right)^{\frac{-Re(p)+iIm(p)}{\left(Re(p)\right)^{2}+\left(Im(p)\right)^{2}}}$$

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

$$m\neq 0$$

Solve for c

$$\left\{\begin{matrix}c=\left(\frac{e}{m}\right)^{\frac{1}{p}}\text{, }&\left(Numerator(p)\text{bmod}2=1\text{ and }Denominator(p)\text{bmod}2=1\text{ and }\left(\frac{e}{m}\right)^{\frac{1}{p}}\neq 0\text{ and }m<0\right)\text{ or }\left(\left(\frac{e}{m}\right)^{\frac{1}{p}}>0\text{ and }p\neq 0\text{ and }m>0\right)\text{ or }\left(\left(\frac{e}{m}\right)^{\frac{1}{p}}<0\text{ and }p\neq 0\text{ and }Denominator(p)\text{bmod}2=1\text{ and }m>0\right)\\c=-\left(\frac{e}{m}\right)^{\frac{1}{p}}\text{, }&\left(m<0\text{ and }Numerator(p)\text{bmod}2=1\text{ and }Numerator(p)\text{bmod}2=0\text{ and }Denominator(p)\text{bmod}2=1\text{ and }\left(\frac{e}{m}\right)^{\frac{1}{p}}\neq 0\right)\text{ or }\left(m>0\text{ and }p\neq 0\text{ and }\left(\frac{e}{m}\right)^{\frac{1}{p}}<0\text{ and }Numerator(p)\text{bmod}2=0\right)\text{ or }\left(m>0\text{ and }p\neq 0\text{ and }\left(\frac{e}{m}\right)^{\frac{1}{p}}>0\text{ and }Numerator(p)\text{bmod}2=0\text{ and }Denominator(p)\text{bmod}2=1\right)\\c\neq 0\text{, }&m=e\text{ and }p=0\end{matrix}\right.$$