Solve 12a^3b^2/7a*14ab/6b^4

$$\frac { 12 a ^ { 3 } b ^ { 2 } } { 7 a } \cdot \frac { 14 a b } { 6 b ^ { 4 } }$$

Evaluate

$$\frac{4a^{3}}{b}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{12a^{2}b^{2}}{7}\times \frac{14ab}{6b^{4}}$$

Cancel out 2b in both numerator and denominator.

$$\frac{12a^{2}b^{2}}{7}\times \frac{7a}{3b^{3}}$$

Multiply \frac{12a^{2}b^{2}}{7} times \frac{7a}{3b^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12a^{2}b^{2}\times 7a}{7\times 3b^{3}}$$

Cancel out 3\times 7b^{2} in both numerator and denominator.

$$\frac{4aa^{2}}{b}$$

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

$$\frac{4a^{3}}{b}$$

Differentiate w.r.t. a

$$\frac{12a^{2}}{b}$$