Solve {l}{y*z*t=x^2}{x*z*t=y^3}{x*y*t=z^3}{x*y*z=t^5}

$$\left. \begin{array} { l } { y \cdot z \cdot t = x ^ { 2 } } \\ { x \cdot z \cdot t = y ^ { 3 } } \\ { x \cdot y \cdot t = z ^ { 3 } } \\ { x \cdot y \cdot z = t ^ { 5 } } \end{array} \right.$$

Solve for y, z, t, x (complex solution)

$$x\neq 0\text{, }y=x^{\frac{3}{4}}\text{, }z=x^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x\neq 0\text{, }y=x^{\frac{3}{4}}\text{, }z=-x^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x\neq 0\text{, }y=-ix^{\frac{3}{4}}\text{, }z=ix^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x\neq 0\text{, }y=-ix^{\frac{3}{4}}\text{, }z=-ix^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x\neq 0\text{, }y=-x^{\frac{3}{4}}\text{, }z=-x^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x\neq 0\text{, }y=-x^{\frac{3}{4}}\text{, }z=x^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x\neq 0\text{, }y=ix^{\frac{3}{4}}\text{, }z=-ix^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x\neq 0\text{, }y=ix^{\frac{3}{4}}\text{, }z=ix^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x=0\text{, }y=0\text{, }z=0\text{, }t=0$$

Solve for y, z, t, x

$$x>0\text{, }y=-x^{\frac{3}{4}}\text{, }z=x^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x>0\text{, }y=-x^{\frac{3}{4}}\text{, }z=-x^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x>0\text{, }y=x^{\frac{3}{4}}\text{, }z=-x^{\frac{3}{4}}\text{, }t=-\sqrt{x}$$

$$x>0\text{, }y=x^{\frac{3}{4}}\text{, }z=x^{\frac{3}{4}}\text{, }t=\sqrt{x}$$

$$x=0\text{, }y=0\text{, }z=0\text{, }t=0$$