Solve 2a^2b^3(-2/3a^3bc^2)

$$2 a ^ { 2 } b ^ { 3 } ( - \frac { 2 } { 3 } a ^ { 3 } b c ^ { 2 } )$$

Evaluate

$$-\frac{4c^{2}b^{4}a^{5}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2a^{5}b^{3}\left(-\frac{2}{3}\right)bc^{2}$$

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

$$2a^{5}b^{4}\left(-\frac{2}{3}\right)c^{2}$$

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

$$-\frac{4}{3}a^{5}b^{4}c^{2}$$

Differentiate w.r.t. c

$$-\frac{8cb^{4}a^{5}}{3}$$