Solve (5a/7b^3)^2

$$( \frac { 5 a } { 7 b ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{25a^{2}}{49b^{6}}$$

Solution Steps

To raise \frac{5a}{7b^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5a\right)^{2}}{\left(7b^{3}\right)^{2}}$$

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

$$\frac{5^{2}a^{2}}{\left(7b^{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{2}}{\left(7b^{3}\right)^{2}}$$

Expand \left(7b^{3}\right)^{2}.

$$\frac{25a^{2}}{7^{2}\left(b^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{25a^{2}}{7^{2}b^{6}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25a^{2}}{49b^{6}}$$

Expand

$$\frac{25a^{2}}{49b^{6}}$$

Solution Steps

To raise \frac{5a}{7b^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5a\right)^{2}}{\left(7b^{3}\right)^{2}}$$

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

$$\frac{5^{2}a^{2}}{\left(7b^{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{2}}{\left(7b^{3}\right)^{2}}$$

Expand \left(7b^{3}\right)^{2}.

$$\frac{25a^{2}}{7^{2}\left(b^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{25a^{2}}{7^{2}b^{6}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{25a^{2}}{49b^{6}}$$