Solve (+11/16xy^2)(-10/11x^4y^3)

$$( + \frac { 11 } { 16 } x y ^ { 2 } ) ( - \frac { 10 } { 11 } x ^ { 4 } y ^ { 3 } )$$

Evaluate

$$-\frac{5\left(xy\right)^{5}}{8}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{11}{16}\right)^{1}x^{1}y^{2}\left(-\frac{10}{11}\right)^{1}x^{4}y^{3}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{11}{16}\right)^{1}\left(-\frac{10}{11}\right)^{1}x^{1}x^{4}y^{2}y^{3}$$

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

$$\left(\frac{11}{16}\right)^{1}\left(-\frac{10}{11}\right)^{1}x^{1+4}y^{2+3}$$

Add the exponents 1 and 4.

$$\left(\frac{11}{16}\right)^{1}\left(-\frac{10}{11}\right)^{1}x^{5}y^{2+3}$$

Add the exponents 2 and 3.

$$\left(\frac{11}{16}\right)^{1}\left(-\frac{10}{11}\right)^{1}x^{5}y^{5}$$

Multiply \frac{11}{16} times -\frac{10}{11} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{5}{8}x^{5}y^{5}$$

Differentiate w.r.t. x

$$-\frac{25x^{4}y^{5}}{8}$$