Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=y^{-\frac{1}{2}}\text{; }x=-y^{-\frac{1}{2}}\text{, }&arg(y^{-\frac{1}{3}})<\frac{2\pi }{3}\text{ and }y\neq 0\end{matrix}\right.
Solve for y (complex solution)
\left\{\begin{matrix}y=-\frac{1}{x^{2}}\text{, }&|-\pi +arg(\sqrt[3]{-\frac{1}{x^{2}}}x^{\frac{2}{3}})|<\frac{2\pi }{3}\text{ and }x\neq 0\\y=\frac{1}{x^{2}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\sqrt{-\frac{1}{y}}\text{; }x=\sqrt{-\frac{1}{y}}\text{, }&y<0\\x=\frac{1}{\sqrt{y}}\text{; }x=-\frac{1}{\sqrt{y}}\text{, }&y>0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=\frac{1}{x^{2}}\text{; }y=-\frac{1}{x^{2}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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Algebra
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\sqrt[ 3 ] { x ^ { 2 } } = x ^ { 2 } \quad \sqrt[ 3 ] { y ^ { 2 } } =
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