Solve 2/3a^{5}b^2*6/7a^2b*14/5a^3b^7

$$\frac { 2 } { 3 } a ^ { 5 } b ^ { 2 } \cdot \frac { 6 } { 7 } a ^ { 2 } b \cdot \frac { 14 } { 5 } a ^ { 3 } b ^ { 7 }$$

Evaluate

$$\frac{8\left(ab\right)^{10}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{2}{3}a^{7}b^{2}\times \frac{6}{7}b\times \frac{14}{5}a^{3}b^{7}$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{2}{3}a^{10}b^{2}\times \frac{6}{7}b\times \frac{14}{5}b^{7}$$

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

$$\frac{2}{3}a^{10}b^{3}\times \frac{6}{7}\times \frac{14}{5}b^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{2}{3}a^{10}b^{10}\times \frac{6}{7}\times \frac{14}{5}$$

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

$$\frac{4}{7}a^{10}b^{10}\times \frac{14}{5}$$

Multiply \frac{4}{7} and \frac{14}{5} to get \frac{8}{5}.

$$\frac{8}{5}a^{10}b^{10}$$

Differentiate w.r.t. a

$$16a^{9}b^{10}$$