Solve A*S:(AS/V)^2/m

$$A \cdot S : \frac { ( \frac { A S } { V } ) ^ { 2 } } { m }$$

Evaluate

$$\frac{mV^{2}}{AS}$$

Solution Steps

Divide AS by \frac{\left(\frac{AS}{V}\right)^{2}}{m} by multiplying AS by the reciprocal of \frac{\left(\frac{AS}{V}\right)^{2}}{m}.

$$\frac{ASm}{\left(\frac{AS}{V}\right)^{2}}$$

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

$$\frac{ASm}{\frac{\left(AS\right)^{2}}{V^{2}}}$$

Divide ASm by \frac{\left(AS\right)^{2}}{V^{2}} by multiplying ASm by the reciprocal of \frac{\left(AS\right)^{2}}{V^{2}}.

$$\frac{ASmV^{2}}{\left(AS\right)^{2}}$$

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

$$\frac{ASmV^{2}}{A^{2}S^{2}}$$

Cancel out AS in both numerator and denominator.

$$\frac{mV^{2}}{AS}$$

Expand

$$\frac{mV^{2}}{AS}$$

Solution Steps

Divide AS by \frac{\left(\frac{AS}{V}\right)^{2}}{m} by multiplying AS by the reciprocal of \frac{\left(\frac{AS}{V}\right)^{2}}{m}.

$$\frac{ASm}{\left(\frac{AS}{V}\right)^{2}}$$

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

$$\frac{ASm}{\frac{\left(AS\right)^{2}}{V^{2}}}$$

Divide ASm by \frac{\left(AS\right)^{2}}{V^{2}} by multiplying ASm by the reciprocal of \frac{\left(AS\right)^{2}}{V^{2}}.

$$\frac{ASmV^{2}}{\left(AS\right)^{2}}$$

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

$$\frac{ASmV^{2}}{A^{2}S^{2}}$$

Cancel out AS in both numerator and denominator.

$$\frac{mV^{2}}{AS}$$