Atrisiniet sqrt[3]{18x^4y^3/12z^3}=y

$$\sqrt[ 3 ] { \frac { 18 x ^ { 4 } y ^ { 3 } } { 12 z ^ { 3 } } } = y$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt[4]{54}z^{\frac{3}{4}}}{3}\text{; }x=-\frac{\sqrt[4]{54}z^{\frac{3}{4}}}{3}\text{, }&z>0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z\neq 0\end{matrix}\right,$$

Atrast y

$$\left\{\begin{matrix}y=0\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&z=\frac{\frac{2^{\frac{2}{3}}}{2}\times \left(3x\right)^{\frac{4}{3}}}{3}\text{ and }x\neq 0\end{matrix}\right,$$