Solve (5xy^3)(-3x^4y)

$$( 5 x y ^ { 3 } ) ( - 3 x ^ { 4 } y )$$

Evaluate

$$-15y^{4}x^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}x^{1}y^{3}\left(-3\right)^{1}x^{4}y^{1}$$

Use the Commutative Property of Multiplication.

$$5^{1}\left(-3\right)^{1}x^{1}x^{4}y^{3}y^{1}$$

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

$$5^{1}\left(-3\right)^{1}x^{1+4}y^{3+1}$$

Add the exponents 1 and 4.

$$5^{1}\left(-3\right)^{1}x^{5}y^{3+1}$$

Add the exponents 3 and 1.

$$5^{1}\left(-3\right)^{1}x^{5}y^{4}$$

Multiply 5 times -3.

$$-15x^{5}y^{4}$$

Differentiate w.r.t. x

$$-75\left(xy\right)^{4}$$