Solve (x^3y^2z)*(-2xy^2)=

$$( x ^ { 3 } y ^ { 2 } z ) \cdot ( - 2 x y ^ { 2 } ) =$$

Evaluate

$$-2z\left(xy\right)^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$z^{1}x^{3}y^{2}\left(-2\right)^{1}x^{1}y^{2}$$

Use the Commutative Property of Multiplication.

$$z^{1}\left(-2\right)^{1}x^{3}x^{1}y^{2}y^{2}$$

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

$$z^{1}\left(-2\right)^{1}x^{3+1}y^{2+2}$$

Add the exponents 3 and 1.

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

Add the exponents 2 and 2.

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

Multiply z times -2.

$$\left(-2z\right)x^{4}y^{4}$$

Differentiate w.r.t. x

$$-8zx^{3}y^{4}$$