Solve x^4yz^2*(-3xy^2)*(1/6y^2z)=

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

Evaluate

$$-\frac{z^{3}\left(xy\right)^{5}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

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

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

Multiply -3 and \frac{1}{6} to get -\frac{1}{2}.

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

Differentiate w.r.t. x

$$-\frac{5z^{3}x^{4}y^{5}}{2}$$