Solve (2/3x^2y)*(1/2xy)=

$$( \frac { 2 } { 3 } x ^ { 2 } y ) \cdot ( \frac { 1 } { 2 } x y ) =$$

Evaluate

$$\frac{y^{2}x^{3}}{3}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 2 and 1.

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

Add the exponents 1 and 1.

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

Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{3}x^{3}y^{2}$$

Differentiate w.r.t. x

$$\left(xy\right)^{2}$$