Solve (-1/8m^3*n^4)(-4/5a^3*m^2n)

$$( - \frac { 1 } { 8 } m ^ { 3 } \cdot n ^ { 4 } ) ( - \frac { 4 } { 5 } a ^ { 3 } \cdot m ^ { 2 } n )$$

Evaluate

$$\frac{a^{3}\left(mn\right)^{5}}{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-\frac{1}{8}m^{5}n^{4}\left(-\frac{4}{5}\right)a^{3}n$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{1}{8}m^{5}n^{5}\left(-\frac{4}{5}\right)a^{3}$$

Multiply -\frac{1}{8} and -\frac{4}{5} to get \frac{1}{10}.

$$\frac{1}{10}m^{5}n^{5}a^{3}$$

Differentiate w.r.t. a

$$\frac{3a^{2}\left(mn\right)^{5}}{10}$$