Solve 4/6*10/x*8/y*2/z

$$\frac { 4 } { 6 } \times \frac { 10 } { x } \times \frac { 8 } { y } \times \frac { 2 } { z }$$

Evaluate

$$\frac{320}{3xyz}$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}\times \frac{10}{x}\times \frac{8}{y}\times \frac{2}{z}$$

Multiply \frac{2}{3} times \frac{10}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 10}{3x}\times \frac{8}{y}\times \frac{2}{z}$$

Multiply \frac{2\times 10}{3x} times \frac{8}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 10\times 8}{3xy}\times \frac{2}{z}$$

Multiply \frac{2\times 10\times 8}{3xy} times \frac{2}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 10\times 8\times 2}{3xyz}$$

Multiply 2 and 10 to get 20.

$$\frac{20\times 8\times 2}{3xyz}$$

Multiply 20 and 8 to get 160.

$$\frac{160\times 2}{3xyz}$$

Multiply 160 and 2 to get 320.

$$\frac{320}{3xyz}$$

Differentiate w.r.t. x

$$-\frac{320}{3yzx^{2}}$$