Solve (2)5ab^3*(-3/4a^3b)*(-2/3a^4b)

$$( 2 ) 5 a b ^ { 3 } \cdot ( - \frac { 3 } { 4 } a ^ { 3 } b ) \cdot ( - \frac { 2 } { 3 } a ^ { 4 } b )$$

Evaluate

$$5b^{5}a^{8}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

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

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

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

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

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

Multiply 2 and 5 to get 10.

$$10a^{8}b^{5}\left(-\frac{3}{4}\right)\left(-\frac{2}{3}\right)$$

Multiply 10 and -\frac{3}{4} to get -\frac{15}{2}.

$$-\frac{15}{2}a^{8}b^{5}\left(-\frac{2}{3}\right)$$

Multiply -\frac{15}{2} and -\frac{2}{3} to get 5.

$$5a^{8}b^{5}$$

Differentiate w.r.t. a

$$40b^{5}a^{7}$$