Solve sqrt[6]{36x^4y^6z^2}=M

$$\sqrt[ 6 ] { 36 x ^ { 4 } y ^ { 6 } z ^ { 2 } } = M$$

Solve for M (complex solution)

$$M=\sqrt[3]{6}\sqrt[6]{z^{2}x^{4}y^{6}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{6}y^{-\frac{3}{2}}z^{-\frac{1}{2}}M^{\frac{3}{2}}}{6}\text{; }x=\frac{\sqrt{6}y^{-\frac{3}{2}}z^{-\frac{1}{2}}M^{\frac{3}{2}}}{6}\text{; }x=\frac{\sqrt{6}iy^{-\frac{3}{2}}z^{-\frac{1}{2}}M^{\frac{3}{2}}}{6}\text{; }x=-\frac{\sqrt{6}iy^{-\frac{3}{2}}z^{-\frac{1}{2}}M^{\frac{3}{2}}}{6}\text{, }&z\neq 0\text{ and }y\neq 0\text{ and }\left(M=0\text{ or }arg(M)<\frac{\pi }{3}\right)\\x\in \mathrm{C}\text{, }&\left(y=0\text{ or }z=0\right)\text{ and }M=0\end{matrix}\right.$$

Solve for M

$$M=\sqrt[3]{6|z|}x^{\frac{2}{3}}|y|$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{-\frac{6\times \left(\frac{M}{y}\right)^{3}}{z}}}{6}\text{; }x=-\frac{\sqrt{-\frac{6\times \left(\frac{M}{y}\right)^{3}}{z}}}{6}\text{, }&M\geq 0\text{ and }\left(z<0\text{ or }M=0\text{ or }y<0\right)\text{ and }y\neq 0\text{ and }z\neq 0\text{ and }\left(y>0\text{ or }M=0\text{ or }z>0\right)\\x=\frac{\sqrt{\frac{6\times \left(\frac{M}{y}\right)^{3}}{z}}}{6}\text{; }x=-\frac{\sqrt{\frac{6\times \left(\frac{M}{y}\right)^{3}}{z}}}{6}\text{, }&y\neq 0\text{ and }z\neq 0\text{ and }M\geq 0\text{ and }\left(y>0\text{ or }z<0\text{ or }M=0\right)\text{ and }\left(M=0\text{ or }z>0\text{ or }y<0\right)\\x\in \mathrm{R}\text{, }&\left(y=0\text{ or }z=0\right)\text{ and }M=0\end{matrix}\right.$$