求解 x^-2x^10/left(x^2right)^4={x}^n

$$\frac{ { x }^{ -2 } { x }^{ 10 } }{ { \left( { x }^{ 2 } \right) }^{ 4 } } = { x }^{ n }$$

求解 n 的值 (复数求解)

$$\left\{\begin{matrix}n=\frac{2\pi n_{1}i}{\ln(x)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 1\text{ and }x\neq 0\\n\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

求解 x 的值 (复数求解)

$$x=e^{-\frac{2\pi n_{1}\left(Im(n)+iRe(n)\right)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}$$

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

求解 n 的值

$$\left\{\begin{matrix}n=0\text{, }&x\neq 0\text{ and }|x|\neq 1\\n\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

求解 x 的值

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=-1\text{, }&Numerator(n)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\\x\neq 0\text{, }&n=0\end{matrix}\right.$$