Solve (12x^2y^4)(1/2x^3y)

$$( 12 x ^ { 2 } y ^ { 4 } ) ( \frac { 1 } { 2 } x ^ { 3 } y )$$

Evaluate

$$6\left(xy\right)^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$12^{1}x^{2}y^{4}\times \left(\frac{1}{2}\right)^{1}x^{3}y^{1}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{2}x^{3}y^{4}y^{1}$$

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

$$12^{1}\times \left(\frac{1}{2}\right)^{1}x^{2+3}y^{4+1}$$

Add the exponents 2 and 3.

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

Add the exponents 4 and 1.

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

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

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

Differentiate w.r.t. x

$$30x^{4}y^{5}$$