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

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

Evaluate

$$15y^{3}x^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}x^{4}y^{1}\times 5^{1}x^{3}y^{2}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times 5^{1}x^{4}x^{3}y^{1}y^{2}$$

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

$$3^{1}\times 5^{1}x^{4+3}y^{1+2}$$

Add the exponents 4 and 3.

$$3^{1}\times 5^{1}x^{7}y^{1+2}$$

Add the exponents 1 and 2.

$$3^{1}\times 5^{1}x^{7}y^{3}$$

Multiply 3 times 5.

$$15x^{7}y^{3}$$

Differentiate w.r.t. x

$$105y^{3}x^{6}$$