Solve (4/3x^2yz)*(1/3y^2zx)*(-6xyz^2)

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

Evaluate

$$-\frac{8\left(xyz\right)^{4}}{3}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Multiply \frac{4}{3} and \frac{1}{3} to get \frac{4}{9}.

$$\frac{4}{9}x^{4}y^{4}z^{4}\left(-6\right)$$

Multiply \frac{4}{9} and -6 to get -\frac{8}{3}.

$$-\frac{8}{3}x^{4}y^{4}z^{4}$$

Differentiate w.r.t. x

$$-\frac{32x^{3}\left(yz\right)^{4}}{3}$$