Solve (2)6a^{4}b^{3}c^2div3a^2b^3*(-2/3ab^2c)

$$( 2 ) 6 a ^ { 4 } b ^ { 3 } c ^ { 2 } \div 3 a ^ { 2 } b ^ { 3 } \cdot ( - \frac { 2 } { 3 } a b ^ { 2 } c )$$

Evaluate

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

Solution Steps

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

$$\frac{2\times 6a^{4}b^{3}c^{2}}{3}a^{3}b^{3}\left(-\frac{2}{3}\right)b^{2}c$$

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

$$\frac{2\times 6a^{4}b^{3}c^{2}}{3}a^{3}b^{5}\left(-\frac{2}{3}\right)c$$

Multiply 2 and 6 to get 12.

$$\frac{12a^{4}b^{3}c^{2}}{3}a^{3}b^{5}\left(-\frac{2}{3}\right)c$$

Divide 12a^{4}b^{3}c^{2} by 3 to get 4a^{4}b^{3}c^{2}.

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

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

$$4a^{7}b^{3}c^{2}b^{5}\left(-\frac{2}{3}\right)c$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$4a^{7}b^{8}c^{2}\left(-\frac{2}{3}\right)c$$

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

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

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

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

Differentiate w.r.t. c

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