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

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

Evaluate

$$12y^{3}x^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 5 and 2.

$$4^{1}\times 3^{1}x^{7}y^{1+2}$$

Add the exponents 1 and 2.

$$4^{1}\times 3^{1}x^{7}y^{3}$$

Multiply 4 times 3.

$$12x^{7}y^{3}$$

Differentiate w.r.t. x

$$84y^{3}x^{6}$$