Solve 8a^{4}b^{3}cdiv2a^2b^3*(-2/3a^3bc^2)

$$8 a ^ { 4 } b ^ { 3 } c \div 2 a ^ { 2 } b ^ { 3 } \cdot ( - \frac { 2 } { 3 } a ^ { 3 } b c ^ { 2 } )$$

Evaluate

$$-\frac{8c^{3}b^{7}a^{9}}{3}$$

Solution Steps

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

$$\frac{8a^{4}b^{3}c}{2}a^{5}b^{3}\left(-\frac{2}{3}\right)bc^{2}$$

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

$$\frac{8a^{4}b^{3}c}{2}a^{5}b^{4}\left(-\frac{2}{3}\right)c^{2}$$

Divide 8a^{4}b^{3}c by 2 to get 4a^{4}b^{3}c.

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

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$4a^{9}b^{3}cb^{4}\left(-\frac{2}{3}\right)c^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$4a^{9}b^{7}c\left(-\frac{2}{3}\right)c^{2}$$

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

$$-\frac{8}{3}a^{9}b^{7}cc^{2}$$

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

$$-\frac{8}{3}a^{9}b^{7}c^{3}$$

Differentiate w.r.t. c

$$-8c^{2}b^{7}a^{9}$$