Solve 6a^4b^3c^2/3/a^2{b^3}2/3a{b}^2c

$$\frac{ \frac{ 6 { a }^{ 4 } { b }^{ 3 } { c }^{ 2 } }{ 3 } }{ { a }^{ 2 } { b }^{ 3 } } \frac{ 2 }{ 3 } a { b }^{ 2 } c$$

Evaluate

$$\frac{4b^{2}\left(ac\right)^{3}}{3}$$

Solution Steps

Express \frac{\frac{6a^{4}b^{3}c^{2}}{3}}{a^{2}b^{3}} as a single fraction.

$$\frac{6a^{4}b^{3}c^{2}}{3a^{2}b^{3}}\times \frac{2}{3}ab^{2}c$$

Cancel out 3a^{2}b^{3} in both numerator and denominator.

$$2a^{2}c^{2}\times \frac{2}{3}ab^{2}c$$

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

$$\frac{4}{3}a^{2}c^{2}ab^{2}c$$

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

$$\frac{4}{3}a^{3}c^{2}b^{2}c$$

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

$$\frac{4}{3}a^{3}c^{3}b^{2}$$

Differentiate w.r.t. a

$$4c^{3}\left(ab\right)^{2}$$