Evaluate: (-4 m ^ 5 n ^ 7) (m n) (-2 m ^ 2 n ^ 6)

Expression: $$( - 4 m ^ { 5 } n ^ { 7 } ) ( m n ) ( - 2 m ^ { 2 } n ^ { 6 } )$$

To multiply powers of the same base, add their exponents. Add $5$ and $1$ to get $6$.

$$-4m^{6}n^{7}n\left(-2\right)m^{2}n^{6}$$

To multiply powers of the same base, add their exponents. Add $6$ and $2$ to get $8$.

$$-4m^{8}n^{7}n\left(-2\right)n^{6}$$

To multiply powers of the same base, add their exponents. Add $7$ and $1$ to get $8$.

$$-4m^{8}n^{8}\left(-2\right)n^{6}$$

To multiply powers of the same base, add their exponents. Add $8$ and $6$ to get $14$.

$$-4m^{8}n^{14}\left(-2\right)$$

Multiply $-4$ and $-2$ to get $8$.

$$8m^{8}n^{14}$$