Solve 3a^2b*(-2a^2b^3)

$$3 a ^ { 2 } b \times ( - 2 a ^ { 2 } b ^ { 3 } )$$

Evaluate

$$-6\left(ab\right)^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}a^{2}b^{1}\left(-2\right)^{1}a^{2}b^{3}$$

Use the Commutative Property of Multiplication.

$$3^{1}\left(-2\right)^{1}a^{2}a^{2}b^{1}b^{3}$$

To multiply powers of the same base, add their exponents.

$$3^{1}\left(-2\right)^{1}a^{2+2}b^{1+3}$$

Add the exponents 2 and 2.

$$3^{1}\left(-2\right)^{1}a^{4}b^{1+3}$$

Add the exponents 1 and 3.

$$3^{1}\left(-2\right)^{1}a^{4}b^{4}$$

Multiply 3 times -2.

$$-6a^{4}b^{4}$$

Differentiate w.r.t. a

$$-24a^{3}b^{4}$$