Solve (-5m^4n^6)(8m^-5n^-3)

$$( - 5 m ^ { 4 } n ^ { 6 } ) ( 8 m ^ { - 5 } n ^ { - 3 } )$$

Evaluate

$$-\frac{40n^{3}}{m}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-5\right)^{1}m^{4}n^{6}\times 8^{1}m^{-5}n^{-3}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{1}\times 8^{1}m^{4}m^{-5}n^{6}n^{-3}$$

To multiply powers of the same base, add their exponents.

$$\left(-5\right)^{1}\times 8^{1}m^{4-5}n^{6-3}$$

Add the exponents 4 and -5.

$$\left(-5\right)^{1}\times 8^{1}\times \frac{1}{m}n^{6-3}$$

Add the exponents 6 and -3.

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

Multiply -5 times 8.

$$-40\times \frac{1}{m}n^{3}$$

Differentiate w.r.t. n

$$-\frac{120n^{2}}{m}$$