Solve (5xy^2)*(2x^2y^3)

$$(5x { y }^{ 2 } ) \times (2 { x }^{ 2 } { y }^{ 3 } )$$

Evaluate

$$10x^{3}y^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 2.

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

Add the exponents 2 and 3.

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

Multiply 5 times 2.

$$10x^{3}y^{5}$$

Differentiate w.r.t. x

$$30x^{2}y^{5}$$