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

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

Evaluate

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

Solution Steps

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

$$-\frac{1}{6}x^{4}y\times \frac{3}{4}y^{2}\times 2xyz^{2}$$

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

$$-\frac{1}{6}x^{5}y\times \frac{3}{4}y^{2}\times 2yz^{2}$$

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

$$-\frac{1}{6}x^{5}y^{3}\times \frac{3}{4}\times 2yz^{2}$$

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

$$-\frac{1}{6}x^{5}y^{4}\times \frac{3}{4}\times 2z^{2}$$

Multiply -\frac{1}{6} and \frac{3}{4} to get -\frac{1}{8}.

$$-\frac{1}{8}x^{5}y^{4}\times 2z^{2}$$

Multiply -\frac{1}{8} and 2 to get -\frac{1}{4}.

$$-\frac{1}{4}x^{5}y^{4}z^{2}$$

Differentiate w.r.t. x

$$-\frac{5z^{2}\left(xy\right)^{4}}{4}$$