Solve (v^2/-2u^4)^5

$$( \frac { v ^ { 2 } } { - 2 u ^ { 4 } } ) ^ { 5 }$$

Evaluate

$$-\frac{v^{10}}{32u^{20}}$$

Solution Steps

To raise \frac{v^{2}}{-2u^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(v^{2}\right)^{5}}{\left(-2u^{4}\right)^{5}}$$

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

$$\frac{v^{10}}{\left(-2u^{4}\right)^{5}}$$

Expand \left(-2u^{4}\right)^{5}.

$$\frac{v^{10}}{\left(-2\right)^{5}\left(u^{4}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{v^{10}}{\left(-2\right)^{5}u^{20}}$$

Calculate -2 to the power of 5 and get -32.

$$\frac{v^{10}}{-32u^{20}}$$

Expand

$$-\frac{v^{10}}{32u^{20}}$$

Solution Steps

To raise \frac{v^{2}}{-2u^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(v^{2}\right)^{5}}{\left(-2u^{4}\right)^{5}}$$

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

$$\frac{v^{10}}{\left(-2u^{4}\right)^{5}}$$

Expand \left(-2u^{4}\right)^{5}.

$$\frac{v^{10}}{\left(-2\right)^{5}\left(u^{4}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{v^{10}}{\left(-2\right)^{5}u^{20}}$$

Calculate -2 to the power of 5 and get -32.

$$\frac{v^{10}}{-32u^{20}}$$