Solve (-/4x^4y)(-1/3x^2y^4)=

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

Evaluate

$$\frac{y^{5}x^{6}}{12}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 4 and 2.

$$\left(-\frac{1}{4}\right)^{1}\left(-\frac{1}{3}\right)^{1}x^{6}y^{1+4}$$

Add the exponents 1 and 4.

$$\left(-\frac{1}{4}\right)^{1}\left(-\frac{1}{3}\right)^{1}x^{6}y^{5}$$

Multiply -\frac{1}{4} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{12}x^{6}y^{5}$$

Differentiate w.r.t. x

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