Solve (4xm^2/5w^2)^2

$$( \frac { 4 x m ^ { 2 } } { 5 w ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{16\times \left(\frac{m}{w}\right)^{4}x^{2}}{25}$$

Solution Steps

To raise \frac{4xm^{2}}{5w^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4xm^{2}\right)^{2}}{\left(5w^{2}\right)^{2}}$$

Expand \left(4xm^{2}\right)^{2}.

$$\frac{4^{2}x^{2}\left(m^{2}\right)^{2}}{\left(5w^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{4^{2}x^{2}m^{4}}{\left(5w^{2}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{2}m^{4}}{\left(5w^{2}\right)^{2}}$$

Expand \left(5w^{2}\right)^{2}.

$$\frac{16x^{2}m^{4}}{5^{2}\left(w^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{16x^{2}m^{4}}{5^{2}w^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16x^{2}m^{4}}{25w^{4}}$$

Expand

$$\frac{16\times \left(\frac{m}{w}\right)^{4}x^{2}}{25}$$

Solution Steps

To raise \frac{4xm^{2}}{5w^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4xm^{2}\right)^{2}}{\left(5w^{2}\right)^{2}}$$

Expand \left(4xm^{2}\right)^{2}.

$$\frac{4^{2}x^{2}\left(m^{2}\right)^{2}}{\left(5w^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{4^{2}x^{2}m^{4}}{\left(5w^{2}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{2}m^{4}}{\left(5w^{2}\right)^{2}}$$

Expand \left(5w^{2}\right)^{2}.

$$\frac{16x^{2}m^{4}}{5^{2}\left(w^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{16x^{2}m^{4}}{5^{2}w^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16x^{2}m^{4}}{25w^{4}}$$