Solve (-5x^4y^2)(4x^5y^4)

$$( - 5 x ^ { 4 } y ^ { 2 } ) ( 4 x ^ { 5 } y ^ { 4 } )$$

Evaluate

$$-20y^{6}x^{9}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-5\right)^{1}x^{4}y^{2}\times 4^{1}x^{5}y^{4}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{1}\times 4^{1}x^{4}x^{5}y^{2}y^{4}$$

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

$$\left(-5\right)^{1}\times 4^{1}x^{4+5}y^{2+4}$$

Add the exponents 4 and 5.

$$\left(-5\right)^{1}\times 4^{1}x^{9}y^{2+4}$$

Add the exponents 2 and 4.

$$\left(-5\right)^{1}\times 4^{1}x^{9}y^{6}$$

Multiply -5 times 4.

$$-20x^{9}y^{6}$$

Differentiate w.r.t. x

$$-180y^{6}x^{8}$$