Solve sum(-2/3a^5b^3c^4):(-4/9abc^2)

$$\sum ( - \frac { 2 } { 3 } a ^ { 5 } b ^ { 3 } c ^ { 4 } ) : ( - \frac { 4 } { 9 } a b c ^ { 2 } )$$

Evaluate

$$\frac{3Σa^{4}\left(bc\right)^{2}}{2}$$

Solution Steps

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

$$\frac{-\frac{2}{3}Σb^{2}c^{2}a^{4}}{-\frac{4}{9}}$$

Divide -\frac{2}{3}Σb^{2}c^{2}a^{4} by -\frac{4}{9} by multiplying -\frac{2}{3}Σb^{2}c^{2}a^{4} by the reciprocal of -\frac{4}{9}.

$$\frac{-\frac{2}{3}Σb^{2}c^{2}a^{4}\times 9}{-4}$$

Multiply -\frac{2}{3} and 9 to get -6.

$$\frac{-6Σb^{2}c^{2}a^{4}}{-4}$$

Divide -6Σb^{2}c^{2}a^{4} by -4 to get \frac{3}{2}Σb^{2}c^{2}a^{4}.

$$\frac{3}{2}Σb^{2}c^{2}a^{4}$$

Differentiate w.r.t. c

$$3cΣb^{2}a^{4}$$