Solve frac{2y^{3}*3xy^{3}}{3x^2y^4}=2y^6*3/3^2x

$$\frac { 2 y ^ { 3 } \cdot 3 x y ^ { 3 } } { 3 x ^ { 2 } y ^ { 4 } } = \frac { 2 y ^ { 6 } \cdot 3 } { 3 ^ { 2 } x }$$

Solve for x (complex solution)

$$x\neq 0$$

$$y=-\sqrt[4]{3}\text{ or }y=\sqrt[4]{3}\text{ or }y=-\sqrt[4]{3}i\text{ or }y=\sqrt[4]{3}i$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x^{2}y^{4}, the least common multiple of 3x^{2}y^{4},3^{2}x.

$$3\times 2y^{3}\times 3xy^{3}=y^{4}x\times 2y^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$3\times 2y^{6}\times 3x=y^{4}x\times 2y^{6}\times 3$$

Multiply 3 and 2 to get 6.

$$6y^{6}\times 3x=y^{4}x\times 2y^{6}\times 3$$

Multiply 6 and 3 to get 18.

$$18y^{6}x=y^{4}x\times 2y^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$18y^{6}x=y^{10}x\times 2\times 3$$

Multiply 2 and 3 to get 6.

$$18y^{6}x=y^{10}x\times 6$$

Subtract y^{10}x\times 6 from both sides.

$$18y^{6}x-y^{10}x\times 6=0$$

Multiply -1 and 6 to get -6.

$$18y^{6}x-6y^{10}x=0$$

Combine all terms containing x.

$$\left(18y^{6}-6y^{10}\right)x=0$$

Divide 0 by 18y^{6}-6y^{10}.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for x

$$x\neq 0$$

$$|y|=\sqrt[4]{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x^{2}y^{4}, the least common multiple of 3x^{2}y^{4},3^{2}x.

$$3\times 2y^{3}\times 3xy^{3}=y^{4}x\times 2y^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$3\times 2y^{6}\times 3x=y^{4}x\times 2y^{6}\times 3$$

Multiply 3 and 2 to get 6.

$$6y^{6}\times 3x=y^{4}x\times 2y^{6}\times 3$$

Multiply 6 and 3 to get 18.

$$18y^{6}x=y^{4}x\times 2y^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$18y^{6}x=y^{10}x\times 2\times 3$$

Multiply 2 and 3 to get 6.

$$18y^{6}x=y^{10}x\times 6$$

Subtract y^{10}x\times 6 from both sides.

$$18y^{6}x-y^{10}x\times 6=0$$

Multiply -1 and 6 to get -6.

$$18y^{6}x-6y^{10}x=0$$

Combine all terms containing x.

$$\left(18y^{6}-6y^{10}\right)x=0$$

Divide 0 by 18y^{6}-6y^{10}.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for y (complex solution)

$$y=\sqrt[4]{3}i$$

$$y=\sqrt[4]{3}$$

$$y=-\sqrt[4]{3}$$

$$y=-\sqrt[4]{3}i\text{, }x\neq 0$$

Solve for y

$$y=\sqrt[4]{3}$$

$$y=-\sqrt[4]{3}\text{, }x\neq 0$$