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

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

Evaluate

$$6\left(ab\right)^{8}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

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

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

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

$$-6a^{7}b^{8}\left(-a\right)$$

Multiply -6 and -1 to get 6.

$$6a^{7}b^{8}a$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$6a^{8}b^{8}$$

Differentiate w.r.t. a

$$48a^{7}b^{8}$$