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

$$( \frac { 2 } { 5 } x ^ { 2 } y ) \cdot ( - \frac { 2 } { 3 } x y )$$

Evaluate

$$-\frac{4y^{2}x^{3}}{15}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{2}{5}\right)^{1}x^{2}y^{1}\left(-\frac{2}{3}\right)^{1}x^{1}y^{1}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{2}{5}\right)^{1}\left(-\frac{2}{3}\right)^{1}x^{2}x^{1}y^{1}y^{1}$$

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

$$\left(\frac{2}{5}\right)^{1}\left(-\frac{2}{3}\right)^{1}x^{2+1}y^{1+1}$$

Add the exponents 2 and 1.

$$\left(\frac{2}{5}\right)^{1}\left(-\frac{2}{3}\right)^{1}x^{3}y^{1+1}$$

Add the exponents 1 and 1.

$$\left(\frac{2}{5}\right)^{1}\left(-\frac{2}{3}\right)^{1}x^{3}y^{2}$$

Multiply \frac{2}{5} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{4}{15}x^{3}y^{2}$$

Differentiate w.r.t. x

$$-\frac{4\left(xy\right)^{2}}{5}$$