Solve y{left(-frac{y/xright)}^2}{2}

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

Evaluate

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

Solution Steps

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

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

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

$$\frac{y\times \frac{y^{2}}{x^{2}}}{2}$$

Express y\times \frac{y^{2}}{x^{2}} as a single fraction.

$$\frac{\frac{yy^{2}}{x^{2}}}{2}$$

Express \frac{\frac{yy^{2}}{x^{2}}}{2} as a single fraction.

$$\frac{yy^{2}}{x^{2}\times 2}$$

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

$$\frac{y^{3}}{x^{2}\times 2}$$

Expand

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

Solution Steps

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

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

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

$$\frac{y\times \frac{y^{2}}{x^{2}}}{2}$$

Express y\times \frac{y^{2}}{x^{2}} as a single fraction.

$$\frac{\frac{yy^{2}}{x^{2}}}{2}$$

Express \frac{\frac{yy^{2}}{x^{2}}}{2} as a single fraction.

$$\frac{yy^{2}}{x^{2}\times 2}$$

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

$$\frac{y^{3}}{x^{2}\times 2}$$