Solve (32uv^-4)^frac{6{5}}

$$( 32 u v ^ { - 4 } ) ^ { \frac { 6 } { 5 } }$$

Evaluate

$$\frac{64u^{\frac{6}{5}}}{v^{\frac{24}{5}}}$$

Solution Steps

Expand \left(32uv^{-4}\right)^{\frac{6}{5}}.

$$32^{\frac{6}{5}}u^{\frac{6}{5}}\left(v^{-4}\right)^{\frac{6}{5}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and \frac{6}{5} to get -\frac{24}{5}.

$$32^{\frac{6}{5}}u^{\frac{6}{5}}v^{-\frac{24}{5}}$$

Calculate 32 to the power of \frac{6}{5} and get 64.

$$64u^{\frac{6}{5}}v^{-\frac{24}{5}}$$

Differentiate w.r.t. u

$$\frac{384\sqrt[5]{u}}{5v^{\frac{24}{5}}}$$