Solve 15x^2y^4(-10x^2y^2)

$$15 x ^ { 2 } y ^ { 4 } ( - 10 x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$-150x^{4}y^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$15^{1}x^{2}y^{4}\left(-10\right)^{1}x^{2}y^{2}$$

Use the Commutative Property of Multiplication.

$$15^{1}\left(-10\right)^{1}x^{2}x^{2}y^{4}y^{2}$$

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

$$15^{1}\left(-10\right)^{1}x^{2+2}y^{4+2}$$

Add the exponents 2 and 2.

$$15^{1}\left(-10\right)^{1}x^{4}y^{4+2}$$

Add the exponents 4 and 2.

$$15^{1}\left(-10\right)^{1}x^{4}y^{6}$$

Multiply 15 times -10.

$$-150x^{4}y^{6}$$

Differentiate w.r.t. x

$$-600x^{3}y^{6}$$