Solve operatorname{ar}(-3x^{2}y^3z)(2x^4y)(-4xy^4z^2)e

$$\operatorname { ar } ( - 3 x ^ { 2 } y ^ { 3 } z ) ( 2 x ^ { 4 } y ) ( - 4 x y ^ { 4 } z ^ { 2 } ) e$$

Evaluate

$$24earz^{3}x^{7}y^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$ar\left(-3\right)x^{6}y^{3}z\times 2y\left(-4\right)xy^{4}z^{2}e$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$ar\left(-3\right)x^{7}y^{3}z\times 2y\left(-4\right)y^{4}z^{2}e$$

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

$$ar\left(-3\right)x^{7}y^{4}z\times 2\left(-4\right)y^{4}z^{2}e$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$ar\left(-3\right)x^{7}y^{8}z\times 2\left(-4\right)z^{2}e$$

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

$$ar\left(-3\right)x^{7}y^{8}z^{3}\times 2\left(-4\right)e$$

Multiply -3 and 2 to get -6.

$$ar\left(-6\right)x^{7}y^{8}z^{3}\left(-4\right)e$$

Multiply -6 and -4 to get 24.

$$ar\times 24x^{7}y^{8}z^{3}e$$

Differentiate w.r.t. x

$$168earz^{3}x^{6}y^{8}$$