Solve (2x/3x^2y^-1)^-2

$$( \frac { 2 x } { 3 x ^ { 2 } y ^ { - 1 } } ) ^ { - 2 }$$

Evaluate

$$\frac{9\times \left(\frac{x}{y}\right)^{2}}{4}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{2}{3\times \frac{1}{y}x}\right)^{-2}$$

Express 3\times \frac{1}{y} as a single fraction.

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

Express \frac{3}{y}x as a single fraction.

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

Divide 2 by \frac{3x}{y} by multiplying 2 by the reciprocal of \frac{3x}{y}.

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

To raise \frac{2y}{3x} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2y\right)^{-2}.

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}y^{-2}}{\left(3x\right)^{-2}}$$

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

$$\frac{\frac{1}{4}y^{-2}}{3^{-2}x^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}y^{-2}}{\frac{1}{9}x^{-2}}$$

Expand

$$\frac{9\times \left(\frac{x}{y}\right)^{2}}{4}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{2}{3\times \frac{1}{y}x}\right)^{-2}$$

Express 3\times \frac{1}{y} as a single fraction.

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

Express \frac{3}{y}x as a single fraction.

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

Divide 2 by \frac{3x}{y} by multiplying 2 by the reciprocal of \frac{3x}{y}.

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

To raise \frac{2y}{3x} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2y\right)^{-2}.

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}y^{-2}}{\left(3x\right)^{-2}}$$

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

$$\frac{\frac{1}{4}y^{-2}}{3^{-2}x^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}y^{-2}}{\frac{1}{9}x^{-2}}$$