Solve 4a^2bc*(-2/3a^3bc^2)

$$4 a ^ { 2 } b c \cdot ( - \frac { 2 } { 3 } a ^ { 3 } b c ^ { 2 } )$$

Evaluate

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

Solution Steps

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

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

Multiply b and b to get b^{2}.

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

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

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

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

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

Differentiate w.r.t. a

$$-\frac{40b^{2}c^{3}a^{4}}{3}$$