Solve (12x^2y^4)(1/2x^5y)

$$(12 { x }^{ 2 } { y }^{ 4 } )( \frac{ 1 }{ 2 } { x }^{ 5 } y)$$

Evaluate

$$6y^{5}x^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$12^{1}x^{2}y^{4}\times \left(\frac{1}{2}\right)^{1}x^{5}y^{1}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{2}x^{5}y^{4}y^{1}$$

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

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{2+5}y^{4+1}$$

Add the exponents 2 and 5.

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{7}y^{4+1}$$

Add the exponents 4 and 1.

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{7}y^{5}$$

Multiply 12 times \frac{1}{2}.

$$6x^{7}y^{5}$$

Differentiate w.r.t. x

$$42y^{5}x^{6}$$