Solve 5x^2y*4x^-1y^-5

$$5 { x }^{ 2 } y \times 4 { x }^{ -1 } { y }^{ -5 }$$

Evaluate

$$\frac{20x}{y^{4}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}x^{2}y^{1}\times 4^{1}\times \frac{1}{x}y^{-5}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times 4^{1}x^{2}\times \frac{1}{x}y^{1}y^{-5}$$

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

$$5^{1}\times 4^{1}x^{2-1}y^{1-5}$$

Add the exponents 2 and -1.

$$5^{1}\times 4^{1}x^{1}y^{1-5}$$

Add the exponents 1 and -5.

$$5^{1}\times 4^{1}xy^{-4}$$

Multiply 5 times 4.

$$20x\times \frac{1}{y^{4}}$$

Differentiate w.r.t. x

$$\frac{20}{y^{4}}$$