Solve (u^3/7v^2)^2

$$( \frac { u ^ { 3 } } { 7 v ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{u^{6}}{49v^{4}}$$

Solution Steps

To raise \frac{u^{3}}{7v^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{3}\right)^{2}}{\left(7v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{\left(7v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{7^{2}\left(v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{7^{2}v^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{u^{6}}{49v^{4}}$$

Expand

$$\frac{u^{6}}{49v^{4}}$$

Solution Steps

To raise \frac{u^{3}}{7v^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{3}\right)^{2}}{\left(7v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{\left(7v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{7^{2}\left(v^{2}\right)^{2}}$$

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

$$\frac{u^{6}}{7^{2}v^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{u^{6}}{49v^{4}}$$