Solve 4xydiv(2x/-y)^2

$$4 x y \div ( \frac { 2 x } { - y } ) ^ { 2 }$$

Evaluate

$$\frac{y^{3}}{x}$$

Short Solution Steps

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

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

Divide 4xy by \frac{\left(2x\right)^{2}}{\left(-y\right)^{2}} by multiplying 4xy by the reciprocal of \frac{\left(2x\right)^{2}}{\left(-y\right)^{2}}.

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

Calculate -y to the power of 2 and get y^{2}.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Cancel out 4x in both numerator and denominator.

$$\frac{y^{3}}{x}$$

Expand

$$\frac{y^{3}}{x}$$

Short Solution Steps

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

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

Divide 4xy by \frac{\left(2x\right)^{2}}{\left(-y\right)^{2}} by multiplying 4xy by the reciprocal of \frac{\left(2x\right)^{2}}{\left(-y\right)^{2}}.

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

Calculate -y to the power of 2 and get y^{2}.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Cancel out 4x in both numerator and denominator.

$$\frac{y^{3}}{x}$$