Solve (-16/5x^4y^3z):(8/25x^2y):(-3/2xy)

$$( - \frac { 16 } { 5 } x ^ { 4 } y ^ { 3 } z ) : ( \frac { 8 } { 25 } x ^ { 2 } y ) : ( - \frac { 3 } { 2 } x y )$$

Evaluate

$$\frac{20xyz}{3}$$

Solution Steps

Express \frac{\frac{-\frac{16}{5}x^{4}y^{3}z}{\frac{8}{25}x^{2}y}}{-\frac{3}{2}xy} as a single fraction.

$$\frac{-\frac{16}{5}x^{4}y^{3}z}{\frac{8}{25}x^{2}y\left(-\frac{3}{2}\right)xy}$$

Cancel out xyyx^{2} in both numerator and denominator.

$$\frac{-\frac{16}{5}xyz}{-\frac{3}{2}\times \frac{8}{25}}$$

Multiply -\frac{3}{2} and \frac{8}{25} to get -\frac{12}{25}.

$$\frac{-\frac{16}{5}xyz}{-\frac{12}{25}}$$

Divide -\frac{16}{5}xyz by -\frac{12}{25} by multiplying -\frac{16}{5}xyz by the reciprocal of -\frac{12}{25}.

$$\frac{-\frac{16}{5}xyz\times 25}{-12}$$

Multiply -\frac{16}{5} and 25 to get -80.

$$\frac{-80xyz}{-12}$$

Divide -80xyz by -12 to get \frac{20}{3}xyz.

$$\frac{20}{3}xyz$$

Differentiate w.r.t. x

$$\frac{20yz}{3}$$