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

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

Evaluate

$$\frac{4a^{10}}{b^{14}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\left(2a^{5}\right)^{2}}{b^{14}}$$

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

$$\frac{2^{2}\left(a^{5}\right)^{2}}{b^{14}}$$

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

$$\frac{2^{2}a^{10}}{b^{14}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{10}}{b^{14}}$$

Expand

$$\frac{4a^{10}}{b^{14}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\left(2a^{5}\right)^{2}}{b^{14}}$$

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

$$\frac{2^{2}\left(a^{5}\right)^{2}}{b^{14}}$$

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

$$\frac{2^{2}a^{10}}{b^{14}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{10}}{b^{14}}$$