Solve (-5x^3y^4)(3x^2y^10)

$$( - 5 x ^ { 3 } y ^ { 4 } ) ( 3 x ^ { 2 } y ^ { 10 } )$$

Evaluate

$$-15x^{5}y^{14}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-5\right)^{1}x^{3}y^{4}\times 3^{1}x^{2}y^{10}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{1}\times 3^{1}x^{3}x^{2}y^{4}y^{10}$$

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

$$\left(-5\right)^{1}\times 3^{1}x^{3+2}y^{4+10}$$

Add the exponents 3 and 2.

$$\left(-5\right)^{1}\times 3^{1}x^{5}y^{4+10}$$

Add the exponents 4 and 10.

$$\left(-5\right)^{1}\times 3^{1}x^{5}y^{14}$$

Multiply -5 times 3.

$$-15x^{5}y^{14}$$

Differentiate w.r.t. x

$$-75x^{4}y^{14}$$