Solve 5x^3y*1/30xy^5

$$5 { x }^{ 3 } y \times \frac{ 1 }{ 30 } x { y }^{ 5 }$$

Evaluate

$$\frac{x^{4}y^{6}}{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}x^{3}y^{1}\times \left(\frac{1}{30}\right)^{1}x^{1}y^{5}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times \left(\frac{1}{30}\right)^{1}x^{3}x^{1}y^{1}y^{5}$$

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

$$5^{1}\times \left(\frac{1}{30}\right)^{1}x^{3+1}y^{1+5}$$

Add the exponents 3 and 1.

$$5^{1}\times \left(\frac{1}{30}\right)^{1}x^{4}y^{1+5}$$

Add the exponents 1 and 5.

$$5^{1}\times \left(\frac{1}{30}\right)^{1}x^{4}y^{6}$$

Multiply 5 times \frac{1}{30}.

$$\frac{1}{6}x^{4}y^{6}$$

Differentiate w.r.t. x

$$\frac{2x^{3}y^{6}}{3}$$