Solve 3x^2yz*(-2xy^2z^3)*(-4)xz^2

$$3 x ^ { 2 } y z \cdot ( - 2 x y ^ { 2 } z ^ { 3 } ) \cdot ( - 4 ) x z ^ { 2 }$$

Evaluate

$$24y^{3}x^{4}z^{6}$$

Solution Steps

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

$$3x^{3}yz\left(-2\right)y^{2}z^{3}\left(-4\right)xz^{2}$$

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

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

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

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

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

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

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

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

Multiply 3 and -2 to get -6.

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

Multiply -6 and -4 to get 24.

$$24x^{4}y^{3}z^{6}$$

Differentiate w.r.t. x

$$96z^{6}\left(xy\right)^{3}$$