Solve (-3x^{2}yz)(-5/9x^{2}y^{2}z)(1/5x^{2}yz^2)]:[(-x^2y)(2x^3yz)(-2/9xyz^2)]

$$( - 3 x ^ { 2 } y z ) ( - \frac { 5 } { 9 } x ^ { 2 } y ^ { 2 } z ) ( \frac { 1 } { 5 } x ^ { 2 } y z ^ { 2 } ) ] : [ ( - x ^ { 2 } y ) ( 2 x ^ { 3 } y z ) ( - \frac { 2 } { 9 } x y z ^ { 2 } ) ]$$

Evaluate

$$\frac{x^{6}\left(yz\right)^{4}}{3}$$

Solution Steps

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

$$-3x^{4}yz\left(-\frac{5}{9}\right)y^{2}z\times \frac{1}{5}x^{2}yz^{2}$$

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

$$-3x^{6}yz\left(-\frac{5}{9}\right)y^{2}z\times \frac{1}{5}yz^{2}$$

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

$$-3x^{6}y^{3}z\left(-\frac{5}{9}\right)z\times \frac{1}{5}yz^{2}$$

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

$$-3x^{6}y^{4}z\left(-\frac{5}{9}\right)z\times \frac{1}{5}z^{2}$$

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

$$-3x^{6}y^{4}z^{2}\left(-\frac{5}{9}\right)\times \frac{1}{5}z^{2}$$

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

$$-3x^{6}y^{4}z^{4}\left(-\frac{5}{9}\right)\times \frac{1}{5}$$

Multiply -3 and -\frac{5}{9} to get \frac{5}{3}.

$$\frac{5}{3}x^{6}y^{4}z^{4}\times \frac{1}{5}$$

Multiply \frac{5}{3} and \frac{1}{5} to get \frac{1}{3}.

$$\frac{1}{3}x^{6}y^{4}z^{4}$$

Differentiate w.r.t. x

$$2x^{5}\left(yz\right)^{4}$$