Solve -6/5xy*15/16yz*8/9xyz

$$\frac{ -6 }{ 5 } xy \times \frac{ 15 }{ 16 } yz \times \frac{ 8 }{ 9 } xyz$$

Evaluate

$$-y^{3}\left(xz\right)^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{-6}{5}x^{2}y\times \frac{15}{16}yz\times \frac{8}{9}yz$$

Multiply y and y to get y^{2}.

$$\frac{-6}{5}x^{2}y^{2}\times \frac{15}{16}z\times \frac{8}{9}yz$$

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

$$\frac{-6}{5}x^{2}y^{3}\times \frac{15}{16}z\times \frac{8}{9}z$$

Multiply z and z to get z^{2}.

$$\frac{-6}{5}x^{2}y^{3}\times \frac{15}{16}z^{2}\times \frac{8}{9}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$-\frac{6}{5}x^{2}y^{3}\times \frac{15}{16}z^{2}\times \frac{8}{9}$$

Multiply -\frac{6}{5} times \frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6\times 15}{5\times 16}x^{2}y^{3}z^{2}\times \frac{8}{9}$$

Do the multiplications in the fraction \frac{-6\times 15}{5\times 16}.

$$\frac{-90}{80}x^{2}y^{3}z^{2}\times \frac{8}{9}$$

Reduce the fraction \frac{-90}{80} to lowest terms by extracting and canceling out 10.

$$-\frac{9}{8}x^{2}y^{3}z^{2}\times \frac{8}{9}$$

Multiply -\frac{9}{8} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 8}{8\times 9}x^{2}y^{3}z^{2}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-9}{9}x^{2}y^{3}z^{2}$$

Divide -9 by 9 to get -1.

$$-x^{2}y^{3}z^{2}$$

Differentiate w.r.t. x

$$-2xz^{2}y^{3}$$