Solve (8a^{4}b^{3}c^{2})(-2/3a^3bc^2)div4a^6b^3c

$$( 8 a ^ { 4 } b ^ { 3 } c ^ { 2 } ) ( - \frac { 2 } { 3 } a ^ { 3 } b c ^ { 2 } ) \div 4 a ^ { 6 } b ^ { 3 } c$$

Evaluate

$$-\frac{4c^{5}b^{7}a^{13}}{3}$$

Solution Steps

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

$$\frac{8a^{7}b^{3}c^{2}\left(-\frac{2}{3}\right)bc^{2}}{4}a^{6}b^{3}c$$

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

$$\frac{8a^{7}b^{4}c^{2}\left(-\frac{2}{3}\right)c^{2}}{4}a^{6}b^{3}c$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{8a^{7}b^{4}c^{4}\left(-\frac{2}{3}\right)}{4}a^{6}b^{3}c$$

Multiply 8 and -\frac{2}{3} to get -\frac{16}{3}.

$$\frac{-\frac{16}{3}a^{7}b^{4}c^{4}}{4}a^{6}b^{3}c$$

Divide -\frac{16}{3}a^{7}b^{4}c^{4} by 4 to get -\frac{4}{3}a^{7}b^{4}c^{4}.

$$-\frac{4}{3}a^{7}b^{4}c^{4}a^{6}b^{3}c$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$-\frac{4}{3}a^{13}b^{4}c^{4}b^{3}c$$

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

$$-\frac{4}{3}a^{13}b^{7}c^{4}c$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{4}{3}a^{13}b^{7}c^{5}$$

Differentiate w.r.t. a

$$-\frac{52c^{5}b^{7}a^{12}}{3}$$