Solve (3)(-2x^2y)*(-1/2xy)*3xyz

$$( 3 ) ( - 2 x ^ { 2 } y ) \cdot ( - \frac { 1 } { 2 } x y ) \cdot 3 x y z$$

Evaluate

$$9zy^{3}x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3\left(-2\right)x^{3}y\left(-\frac{1}{2}\right)y\times 3xyz$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$3\left(-2\right)x^{4}y\left(-\frac{1}{2}\right)y\times 3yz$$

Multiply y and y to get y^{2}.

$$3\left(-2\right)x^{4}y^{2}\left(-\frac{1}{2}\right)\times 3yz$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3\left(-2\right)x^{4}y^{3}\left(-\frac{1}{2}\right)\times 3z$$

Multiply 3 and -2 to get -6.

$$-6x^{4}y^{3}\left(-\frac{1}{2}\right)\times 3z$$

Multiply -6 and -\frac{1}{2} to get 3.

$$3x^{4}y^{3}\times 3z$$

Multiply 3 and 3 to get 9.

$$9x^{4}y^{3}z$$

Differentiate w.r.t. x

$$36z\left(xy\right)^{3}$$