Solve (64m^-6n^3)^2/3

$$( 64 m ^ { - 6 } n ^ { 3 } ) ^ { 2 / 3 }$$

Evaluate

$$\frac{16n^{2}}{m^{4}}$$

Solution Steps

Expand \left(64m^{-6}n^{3}\right)^{\frac{2}{3}}.

$$64^{\frac{2}{3}}\left(m^{-6}\right)^{\frac{2}{3}}\left(n^{3}\right)^{\frac{2}{3}}$$

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

$$64^{\frac{2}{3}}m^{-4}\left(n^{3}\right)^{\frac{2}{3}}$$

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

$$64^{\frac{2}{3}}m^{-4}n^{2}$$

Calculate 64 to the power of \frac{2}{3} and get 16.

$$16m^{-4}n^{2}$$

Differentiate w.r.t. m

$$-\frac{64n^{2}}{m^{5}}$$