Solve (-2/5xy^3)(-3x^2z)(-5/6yz^3)

$$( - \frac { 2 } { 5 } x y ^ { 3 } ) ( - 3 x ^ { 2 } z ) ( - \frac { 5 } { 6 } y z ^ { 3 } )$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

Multiply -\frac{2}{5} and -3 to get \frac{6}{5}.

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

Multiply \frac{6}{5} and -\frac{5}{6} to get -1.

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

Differentiate w.r.t. x

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