Solve (8x^3v^2)(-3x^2v^3)

$$( 8 x ^ { 3 } v ^ { 2 } ) ( - 3 x ^ { 2 } v ^ { 3 } )$$

Evaluate

$$-24\left(vx\right)^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$8^{1}x^{3}v^{2}\left(-3\right)^{1}x^{2}v^{3}$$

Use the Commutative Property of Multiplication.

$$8^{1}\left(-3\right)^{1}x^{3}x^{2}v^{2}v^{3}$$

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

$$8^{1}\left(-3\right)^{1}x^{3+2}v^{2+3}$$

Add the exponents 3 and 2.

$$8^{1}\left(-3\right)^{1}x^{5}v^{2+3}$$

Add the exponents 2 and 3.

$$8^{1}\left(-3\right)^{1}x^{5}v^{5}$$

Multiply 8 times -3.

$$-24x^{5}v^{5}$$

Differentiate w.r.t. x

$$-120x^{4}v^{5}$$