Solve (-2a^3x)(4a^2x^7)

$$( - 2 a ^ { 3 } x ) ( 4 a ^ { 2 } x ^ { 7 } )$$

Evaluate

$$-8a^{5}x^{8}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-2\right)^{1}a^{3}x^{1}\times 4^{1}a^{2}x^{7}$$

Use the Commutative Property of Multiplication.

$$\left(-2\right)^{1}\times 4^{1}a^{3}a^{2}x^{1}x^{7}$$

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

$$\left(-2\right)^{1}\times 4^{1}a^{3+2}x^{1+7}$$

Add the exponents 3 and 2.

$$\left(-2\right)^{1}\times 4^{1}a^{5}x^{1+7}$$

Add the exponents 1 and 7.

$$\left(-2\right)^{1}\times 4^{1}a^{5}x^{8}$$

Multiply -2 times 4.

$$-8a^{5}x^{8}$$

Differentiate w.r.t. x

$$-64a^{5}x^{7}$$