Solve (u^4v^6)^-2/3

$$( u ^ { 4 } v ^ { 6 } ) ^ { - 2 / 3 }$$

Evaluate

$$\frac{1}{u^{\frac{8}{3}}v^{4}}$$

Solution Steps

Expand \left(u^{4}v^{6}\right)^{-\frac{2}{3}}.

$$\left(u^{4}\right)^{-\frac{2}{3}}\left(v^{6}\right)^{-\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -\frac{2}{3} to get -\frac{8}{3}.

$$u^{-\frac{8}{3}}\left(v^{6}\right)^{-\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -\frac{2}{3} to get -4.

$$u^{-\frac{8}{3}}v^{-4}$$

Differentiate w.r.t. u

$$-\frac{8}{3u^{\frac{11}{3}}v^{4}}$$