Solve 2(+3/8ab)(-3bc/4):(-1/2abm^2)(-7/3bm^2)(-2b^2)

$$2 ( + \frac { 3 } { 8 } a b ) ( - \frac { 3 b c } { 4 } ) : ( - \frac { 1 } { 2 } a b m ^ { 2 } ) ( - \frac { 7 } { 3 } b m ^ { 2 } ) ( - 2 b ^ { 2 } )$$

Evaluate

$$\frac{21cb^{4}}{4}$$

Solution Steps

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

$$\frac{2\times \frac{3}{8}ab\left(-\frac{3bc}{4}\right)}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Multiply 2 and \frac{3}{8} to get \frac{3}{4}.

$$\frac{\frac{3}{4}ab\left(-\frac{3bc}{4}\right)}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Multiply \frac{3}{4} times -\frac{3bc}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-3\times 3bc}{4\times 4}ab}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Multiply -3 and 3 to get -9.

$$\frac{\frac{-9bc}{4\times 4}ab}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Multiply 4 and 4 to get 16.

$$\frac{\frac{-9bc}{16}ab}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Express \frac{-9bc}{16}a as a single fraction.

$$\frac{\frac{-9bca}{16}b}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Express \frac{-9bca}{16}b as a single fraction.

$$\frac{\frac{-9bcab}{16}}{-\frac{1}{2}abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Express \frac{\frac{-9bcab}{16}}{-\frac{1}{2}abm^{2}} as a single fraction.

$$\frac{-9bcab}{16\left(-\frac{1}{2}\right)abm^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Cancel out ab in both numerator and denominator.

$$\frac{-9bc}{-\frac{1}{2}\times 16m^{2}}\left(-\frac{7}{3}\right)b^{3}m^{2}\left(-2\right)$$

Multiply -\frac{7}{3} and -2 to get \frac{14}{3}.

$$\frac{-9bc}{-\frac{1}{2}\times 16m^{2}}\times \frac{14}{3}b^{3}m^{2}$$

Multiply -\frac{1}{2} and 16 to get -8.

$$\frac{-9bc}{-8m^{2}}\times \frac{14}{3}b^{3}m^{2}$$

Multiply \frac{-9bc}{-8m^{2}} times \frac{14}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9bc\times 14}{-8m^{2}\times 3}b^{3}m^{2}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{-3\times 7bc}{-4m^{2}}b^{3}m^{2}$$

Express \frac{-3\times 7bc}{-4m^{2}}b^{3} as a single fraction.

$$\frac{-3\times 7bcb^{3}}{-4m^{2}}m^{2}$$

Express \frac{-3\times 7bcb^{3}}{-4m^{2}}m^{2} as a single fraction.

$$\frac{-3\times 7bcb^{3}m^{2}}{-4m^{2}}$$

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

$$\frac{-3\times 7bcb^{3}}{-4}$$

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

$$\frac{-3\times 7b^{4}c}{-4}$$

Multiply -3 and 7 to get -21.

$$\frac{-21b^{4}c}{-4}$$

Differentiate w.r.t. c

$$\frac{21b^{4}}{4}$$