Solve (4uv^-frac{1{2}})^4

$$( 4 u v ^ { - \frac { 1 } { 2 } } ) ^ { 4 }$$

Evaluate

$$\frac{256u^{4}}{v^{2}}$$

Solution Steps

Expand \left(4uv^{-\frac{1}{2}}\right)^{4}.

$$4^{4}u^{4}\left(v^{-\frac{1}{2}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and 4 to get -2.

$$4^{4}u^{4}v^{-2}$$

Calculate 4 to the power of 4 and get 256.

$$256u^{4}v^{-2}$$

Expand

$$\frac{256u^{4}}{v^{2}}$$

Solution Steps

Expand \left(4uv^{-\frac{1}{2}}\right)^{4}.

$$4^{4}u^{4}\left(v^{-\frac{1}{2}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and 4 to get -2.

$$4^{4}u^{4}v^{-2}$$

Calculate 4 to the power of 4 and get 256.

$$256u^{4}v^{-2}$$