Solve (-8a^3b^2)(4ab^3)

$$( - 8 a ^ { 3 } b ^ { 2 } ) ( 4 a b ^ { 3 } )$$

Evaluate

$$-32a^{4}b^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-8\right)^{1}a^{3}b^{2}\times 4^{1}a^{1}b^{3}$$

Use the Commutative Property of Multiplication.

$$\left(-8\right)^{1}\times 4^{1}a^{3}a^{1}b^{2}b^{3}$$

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

$$\left(-8\right)^{1}\times 4^{1}a^{3+1}b^{2+3}$$

Add the exponents 3 and 1.

$$\left(-8\right)^{1}\times 4^{1}a^{4}b^{2+3}$$

Add the exponents 2 and 3.

$$\left(-8\right)^{1}\times 4^{1}a^{4}b^{5}$$

Multiply -8 times 4.

$$-32a^{4}b^{5}$$

Differentiate w.r.t. a

$$-128a^{3}b^{5}$$