Solve (m^-frac{1{4}}*n^-frac{5{6}})^-frac{12{5}}

$$( m ^ { - \frac { 1 } { 4 } } \cdot n ^ { - \frac { 5 } { 6 } } ) ^ { - \frac { 12 } { 5 } }$$

Evaluate

$$m^{\frac{3}{5}}n^{2}$$

Solution Steps

Expand \left(m^{-\frac{1}{4}}n^{-\frac{5}{6}}\right)^{-\frac{12}{5}}.

$$\left(m^{-\frac{1}{4}}\right)^{-\frac{12}{5}}\left(n^{-\frac{5}{6}}\right)^{-\frac{12}{5}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{4} and -\frac{12}{5} to get \frac{3}{5}.

$$m^{\frac{3}{5}}\left(n^{-\frac{5}{6}}\right)^{-\frac{12}{5}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{6} and -\frac{12}{5} to get 2.

$$m^{\frac{3}{5}}n^{2}$$

Differentiate w.r.t. m

$$\frac{3n^{2}}{5m^{\frac{2}{5}}}$$