Solve (7/4a^{6}b^8c^2)(2/3a^2b^5c)

$$( \frac { 7 } { 4 } a ^ { 6 } b ^ { 8 } c ^ { 2 } ) ( \frac { 2 } { 3 } a ^ { 2 } b ^ { 5 } c )$$

Evaluate

$$\frac{7c^{3}a^{8}b^{13}}{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{7}{4}a^{8}b^{8}c^{2}\times \frac{2}{3}b^{5}c$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$\frac{7}{4}a^{8}b^{13}c^{2}\times \frac{2}{3}c$$

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

$$\frac{7}{4}a^{8}b^{13}c^{3}\times \frac{2}{3}$$

Multiply \frac{7}{4} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{7}{6}a^{8}b^{13}c^{3}$$

Differentiate w.r.t. a

$$\frac{28c^{3}a^{7}b^{13}}{3}$$