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

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

Evaluate

$$6x^{2}y^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 4 and -2.

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

Add the exponents 1 and 5.

$$2^{1}\times 3^{1}x^{2}y^{6}$$

Multiply 2 times 3.

$$6x^{2}y^{6}$$

Differentiate w.r.t. x

$$12xy^{6}$$