Solve (-uv)^-frac{2{3}}

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

Evaluate

$$\frac{1}{\left(uv\right)^{\frac{2}{3}}}$$

Solution Steps

Expand \left(\left(-u\right)v\right)^{-\frac{2}{3}}.

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

Expand \left(-u\right)^{-\frac{2}{3}}.

$$\left(-1\right)^{-\frac{2}{3}}u^{-\frac{2}{3}}v^{-\frac{2}{3}}$$

Calculate -1 to the power of -\frac{2}{3} and get 1.

$$1u^{-\frac{2}{3}}v^{-\frac{2}{3}}$$

For any term t, t\times 1=t and 1t=t.

$$u^{-\frac{2}{3}}v^{-\frac{2}{3}}$$

Differentiate w.r.t. u

$$-\frac{2}{3v^{\frac{2}{3}}u^{\frac{5}{3}}}$$