Solve (5x/7y^2)^2

$$( \frac { 5 x } { 7 y ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{25x^{2}}{49y^{4}}$$

Solution Steps

To raise \frac{5x}{7y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x\right)^{2}}{\left(7y^{2}\right)^{2}}$$

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

$$\frac{5^{2}x^{2}}{\left(7y^{2}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{2}}{\left(7y^{2}\right)^{2}}$$

Expand \left(7y^{2}\right)^{2}.

$$\frac{25x^{2}}{7^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{25x^{2}}{7^{2}y^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25x^{2}}{49y^{4}}$$

Expand

$$\frac{25x^{2}}{49y^{4}}$$

Solution Steps

To raise \frac{5x}{7y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x\right)^{2}}{\left(7y^{2}\right)^{2}}$$

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

$$\frac{5^{2}x^{2}}{\left(7y^{2}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{2}}{\left(7y^{2}\right)^{2}}$$

Expand \left(7y^{2}\right)^{2}.

$$\frac{25x^{2}}{7^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{25x^{2}}{7^{2}y^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25x^{2}}{49y^{4}}$$