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

$$( - r s ) ^ { \frac { 2 } { 3 } }$$

Evaluate

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

Solution Steps

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

$$\left(-r\right)^{\frac{2}{3}}s^{\frac{2}{3}}$$

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

$$\left(-1\right)^{\frac{2}{3}}r^{\frac{2}{3}}s^{\frac{2}{3}}$$

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

$$1r^{\frac{2}{3}}s^{\frac{2}{3}}$$

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

$$r^{\frac{2}{3}}s^{\frac{2}{3}}$$

Differentiate w.r.t. r

$$\frac{2s^{\frac{2}{3}}}{3\sqrt[3]{r}}$$