Solve (-4m^3n^5)(-3m^-1n^-2)

$$( - 4 m ^ { 3 } n ^ { 5 } ) ( - 3 m ^ { - 1 } n ^ { - 2 } )$$

Evaluate

$$12m^{2}n^{3}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}m^{3}n^{5}\left(-3\right)^{1}\times \frac{1}{m}n^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\left(-3\right)^{1}m^{3}\times \frac{1}{m}n^{5}n^{-2}$$

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

$$\left(-4\right)^{1}\left(-3\right)^{1}m^{3-1}n^{5-2}$$

Add the exponents 3 and -1.

$$\left(-4\right)^{1}\left(-3\right)^{1}m^{2}n^{5-2}$$

Add the exponents 5 and -2.

$$\left(-4\right)^{1}\left(-3\right)^{1}m^{2}n^{3}$$

Multiply -4 times -3.

$$12m^{2}n^{3}$$

Differentiate w.r.t. n

$$36\left(mn\right)^{2}$$