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

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

Evaluate

$$-20m^{3}n^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 2.

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

Add the exponents 3 and 2.

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

Multiply -5 times 4.

$$-20m^{3}n^{5}$$

Differentiate w.r.t. m

$$-60m^{2}n^{5}$$