Solve 3ab^2(-4a^3b^4)=

$$3 a b ^ { 2 } ( - 4 a ^ { 3 } b ^ { 4 } ) =$$

Evaluate

$$-12a^{4}b^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 3.

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

Add the exponents 2 and 4.

$$3^{1}\left(-4\right)^{1}a^{4}b^{6}$$

Multiply 3 times -4.

$$-12a^{4}b^{6}$$

Differentiate w.r.t. a

$$-48a^{3}b^{6}$$