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

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

Evaluate

$$\frac{25a^{4}}{49y^{10}}$$

Solution Steps

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

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

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

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

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

$$\frac{5^{2}a^{4}}{\left(7y^{5}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{4}}{\left(7y^{5}\right)^{2}}$$

Expand \left(7y^{5}\right)^{2}.

$$\frac{25a^{4}}{7^{2}\left(y^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{25a^{4}}{7^{2}y^{10}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25a^{4}}{49y^{10}}$$

Expand

$$\frac{25a^{4}}{49y^{10}}$$

Solution Steps

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

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

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

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

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

$$\frac{5^{2}a^{4}}{\left(7y^{5}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{4}}{\left(7y^{5}\right)^{2}}$$

Expand \left(7y^{5}\right)^{2}.

$$\frac{25a^{4}}{7^{2}\left(y^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{25a^{4}}{7^{2}y^{10}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25a^{4}}{49y^{10}}$$