Solve (-3wp^2/5d^2)^2

$$( \frac { - 3 w p ^ { 2 } } { 5 d ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{9\times \left(\frac{p}{d}\right)^{4}w^{2}}{25}$$

Solution Steps

To raise \frac{-3wp^{2}}{5d^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3wp^{2}\right)^{2}}{\left(5d^{2}\right)^{2}}$$

Expand \left(-3wp^{2}\right)^{2}.

$$\frac{\left(-3\right)^{2}w^{2}\left(p^{2}\right)^{2}}{\left(5d^{2}\right)^{2}}$$

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

$$\frac{\left(-3\right)^{2}w^{2}p^{4}}{\left(5d^{2}\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9w^{2}p^{4}}{\left(5d^{2}\right)^{2}}$$

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

$$\frac{9w^{2}p^{4}}{5^{2}\left(d^{2}\right)^{2}}$$

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

$$\frac{9w^{2}p^{4}}{5^{2}d^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{9w^{2}p^{4}}{25d^{4}}$$

Expand

$$\frac{9\times \left(\frac{p}{d}\right)^{4}w^{2}}{25}$$

Solution Steps

To raise \frac{-3wp^{2}}{5d^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3wp^{2}\right)^{2}}{\left(5d^{2}\right)^{2}}$$

Expand \left(-3wp^{2}\right)^{2}.

$$\frac{\left(-3\right)^{2}w^{2}\left(p^{2}\right)^{2}}{\left(5d^{2}\right)^{2}}$$

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

$$\frac{\left(-3\right)^{2}w^{2}p^{4}}{\left(5d^{2}\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9w^{2}p^{4}}{\left(5d^{2}\right)^{2}}$$

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

$$\frac{9w^{2}p^{4}}{5^{2}\left(d^{2}\right)^{2}}$$

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

$$\frac{9w^{2}p^{4}}{5^{2}d^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{9w^{2}p^{4}}{25d^{4}}$$