Solve (-2uv/w^4)^6

$$( \frac { - 2 u v } { w ^ { 4 } } ) ^ { 6 }$$

Evaluate

$$\frac{64\left(uv\right)^{6}}{w^{24}}$$

Solution Steps

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

$$\frac{\left(-2uv\right)^{6}}{\left(w^{4}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{\left(-2uv\right)^{6}}{w^{24}}$$

Expand \left(-2uv\right)^{6}.

$$\frac{\left(-2\right)^{6}u^{6}v^{6}}{w^{24}}$$

Calculate -2 to the power of 6 and get 64.

$$\frac{64u^{6}v^{6}}{w^{24}}$$

Expand

$$\frac{64\left(uv\right)^{6}}{w^{24}}$$

Solution Steps

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

$$\frac{\left(-2uv\right)^{6}}{\left(w^{4}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{\left(-2uv\right)^{6}}{w^{24}}$$

Expand \left(-2uv\right)^{6}.

$$\frac{\left(-2\right)^{6}u^{6}v^{6}}{w^{24}}$$

Calculate -2 to the power of 6 and get 64.

$$\frac{64u^{6}v^{6}}{w^{24}}$$