Solve (2500frac{m^2/s^2)(frac{sqrt{2}}{2})^2}{20m}

$$\frac { ( 2500 \frac { m ^ { 2 } } { s ^ { 2 } } ) ( \frac { \sqrt { 2 } } { 2 } ) ^ { 2 } } { 20 m }$$

Evaluate

$$\frac{125m}{2s^{2}}$$

Short Solution Steps

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

$$\frac{2500\times \frac{m^{2}}{s^{2}}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{20m}$$

Express 2500\times \frac{m^{2}}{s^{2}} as a single fraction.

$$\frac{\frac{2500m^{2}}{s^{2}}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{20m}$$

Multiply \frac{2500m^{2}}{s^{2}} times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}}}{20m}$$

Express \frac{\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}}}{20m} as a single fraction.

$$\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}\times 20m}$$

Cancel out 20m in both numerator and denominator.

$$\frac{125\left(\sqrt{2}\right)^{2}m}{2^{2}s^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{125\times 2m}{2^{2}s^{2}}$$

Multiply 125 and 2 to get 250.

$$\frac{250m}{2^{2}s^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{250m}{4s^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{125m}{2s^{2}}$$

Expand

$$\frac{125m}{2s^{2}}$$

Short Solution Steps

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

$$\frac{2500\times \frac{m^{2}}{s^{2}}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{20m}$$

Express 2500\times \frac{m^{2}}{s^{2}} as a single fraction.

$$\frac{\frac{2500m^{2}}{s^{2}}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{20m}$$

Multiply \frac{2500m^{2}}{s^{2}} times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}}}{20m}$$

Express \frac{\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}}}{20m} as a single fraction.

$$\frac{2500m^{2}\left(\sqrt{2}\right)^{2}}{s^{2}\times 2^{2}\times 20m}$$

Cancel out 20m in both numerator and denominator.

$$\frac{125\left(\sqrt{2}\right)^{2}m}{2^{2}s^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{125\times 2m}{2^{2}s^{2}}$$

Multiply 125 and 2 to get 250.

$$\frac{250m}{2^{2}s^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{250m}{4s^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{125m}{2s^{2}}$$