Solve b^2/1^3*(-10a/16ab)*2/b^3

$$\frac { b ^ { 2 } } { 1 ^ { 3 } } \cdot ( - \frac { 10 a } { 16 a b } ) \cdot \frac { 2 } { b ^ { 3 } }$$

Evaluate

$$-\frac{5}{4b^{2}}$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\frac{b^{2}}{1}\left(-\frac{10a}{16ab}\right)\times \frac{2}{b^{3}}$$

Anything divided by one gives itself.

$$b^{2}\left(-\frac{10a}{16ab}\right)\times \frac{2}{b^{3}}$$

Cancel out 2a in both numerator and denominator.

$$b^{2}\left(-\frac{5}{8b}\right)\times \frac{2}{b^{3}}$$

Express b^{2}\left(-\frac{5}{8b}\right) as a single fraction.

$$\frac{-b^{2}\times 5}{8b}\times \frac{2}{b^{3}}$$

Cancel out b in both numerator and denominator.

$$\frac{-5b}{8}\times \frac{2}{b^{3}}$$

Multiply \frac{-5b}{8} times \frac{2}{b^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5b\times 2}{8b^{3}}$$

Cancel out 2b in both numerator and denominator.

$$\frac{-5}{4b^{2}}$$

Differentiate w.r.t. b

$$\frac{5}{2b^{3}}$$