Solve (-8/3x^5y^2)(+9/2xy)

$$( - \frac { 8 } { 3 } x ^ { 5 } y ^ { 2 } ) ( + \frac { 9 } { 2 } x y )$$

Evaluate

$$-12y^{3}x^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-\frac{8}{3}\right)^{1}x^{5}y^{2}\times \left(\frac{9}{2}\right)^{1}x^{1}y^{1}$$

Use the Commutative Property of Multiplication.

$$\left(-\frac{8}{3}\right)^{1}\times \left(\frac{9}{2}\right)^{1}x^{5}x^{1}y^{2}y^{1}$$

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

$$\left(-\frac{8}{3}\right)^{1}\times \left(\frac{9}{2}\right)^{1}x^{5+1}y^{2+1}$$

Add the exponents 5 and 1.

$$\left(-\frac{8}{3}\right)^{1}\times \left(\frac{9}{2}\right)^{1}x^{6}y^{2+1}$$

Add the exponents 2 and 1.

$$\left(-\frac{8}{3}\right)^{1}\times \left(\frac{9}{2}\right)^{1}x^{6}y^{3}$$

Multiply -\frac{8}{3} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-12x^{6}y^{3}$$

Differentiate w.r.t. x

$$-72y^{3}x^{5}$$