Solve (-y/3x)^2*(-2x^2/y)^2

$$( - \frac { y } { 3 x } ) ^ { 2 } \cdot ( - \frac { 2 x ^ { 2 } } { y } ) ^ { 2 }$$

Evaluate

$$\frac{4x^{2}}{9}$$

Solution Steps

Calculate -\frac{y}{3x} to the power of 2 and get \left(\frac{y}{3x}\right)^{2}.

$$\left(\frac{y}{3x}\right)^{2}\left(-\frac{2x^{2}}{y}\right)^{2}$$

Calculate -\frac{2x^{2}}{y} to the power of 2 and get \left(\frac{2x^{2}}{y}\right)^{2}.

$$\left(\frac{y}{3x}\right)^{2}\times \left(\frac{2x^{2}}{y}\right)^{2}$$

To raise \frac{y}{3x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{y^{2}}{\left(3x\right)^{2}}\times \left(\frac{2x^{2}}{y}\right)^{2}$$

To raise \frac{2x^{2}}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{y^{2}}{\left(3x\right)^{2}}\times \frac{\left(2x^{2}\right)^{2}}{y^{2}}$$

Multiply \frac{y^{2}}{\left(3x\right)^{2}} times \frac{\left(2x^{2}\right)^{2}}{y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y^{2}\times \left(2x^{2}\right)^{2}}{\left(3x\right)^{2}y^{2}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{\left(2x^{2}\right)^{2}}{\left(3x\right)^{2}}$$

Expand \left(2x^{2}\right)^{2}.

$$\frac{2^{2}\left(x^{2}\right)^{2}}{\left(3x\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{2^{2}x^{4}}{\left(3x\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}}{\left(3x\right)^{2}}$$

Expand \left(3x\right)^{2}.

$$\frac{4x^{4}}{3^{2}x^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{4}}{9x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{4x^{2}}{9}$$

Expand

$$\frac{4x^{2}}{9}$$

Solution Steps

Calculate -\frac{y}{3x} to the power of 2 and get \left(\frac{y}{3x}\right)^{2}.

$$\left(\frac{y}{3x}\right)^{2}\left(-\frac{2x^{2}}{y}\right)^{2}$$

Calculate -\frac{2x^{2}}{y} to the power of 2 and get \left(\frac{2x^{2}}{y}\right)^{2}.

$$\left(\frac{y}{3x}\right)^{2}\times \left(\frac{2x^{2}}{y}\right)^{2}$$

To raise \frac{y}{3x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{y^{2}}{\left(3x\right)^{2}}\times \left(\frac{2x^{2}}{y}\right)^{2}$$

To raise \frac{2x^{2}}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{y^{2}}{\left(3x\right)^{2}}\times \frac{\left(2x^{2}\right)^{2}}{y^{2}}$$

Multiply \frac{y^{2}}{\left(3x\right)^{2}} times \frac{\left(2x^{2}\right)^{2}}{y^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y^{2}\times \left(2x^{2}\right)^{2}}{\left(3x\right)^{2}y^{2}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{\left(2x^{2}\right)^{2}}{\left(3x\right)^{2}}$$

Expand \left(2x^{2}\right)^{2}.

$$\frac{2^{2}\left(x^{2}\right)^{2}}{\left(3x\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{2^{2}x^{4}}{\left(3x\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}}{\left(3x\right)^{2}}$$

Expand \left(3x\right)^{2}.

$$\frac{4x^{4}}{3^{2}x^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{4}}{9x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{4x^{2}}{9}$$