Solve -12x^2y^2(10x^3y^2)

$$- 12 x ^ { 2 } y ^ { 2 } ( 10 x ^ { 3 } y ^ { 2 } )$$

Evaluate

$$-120y^{4}x^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-12\right)^{1}x^{2}y^{2}\times 10^{1}x^{3}y^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-12\right)^{1}\times 10^{1}x^{2}x^{3}y^{2}y^{2}$$

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

$$\left(-12\right)^{1}\times 10^{1}x^{2+3}y^{2+2}$$

Add the exponents 2 and 3.

$$\left(-12\right)^{1}\times 10^{1}x^{5}y^{2+2}$$

Add the exponents 2 and 2.

$$\left(-12\right)^{1}\times 10^{1}x^{5}y^{4}$$

Multiply -12 times 10.

$$-120x^{5}y^{4}$$

Differentiate w.r.t. x

$$-600\left(xy\right)^{4}$$