Solve (4x^-5y)(2x^2y^-3)

$$( 4 x ^ { - 5 } y ) ( 2 x ^ { 2 } y ^ { - 3 } )$$

Evaluate

$$\frac{8}{y^{2}x^{3}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$4^{1}x^{-5}y^{1}\times 2^{1}x^{2}y^{-3}$$

Use the Commutative Property of Multiplication.

$$4^{1}\times 2^{1}x^{-5}x^{2}y^{1}y^{-3}$$

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

$$4^{1}\times 2^{1}x^{-5+2}y^{1-3}$$

Add the exponents -5 and 2.

$$4^{1}\times 2^{1}x^{-3}y^{1-3}$$

Add the exponents 1 and -3.

$$4^{1}\times 2^{1}\times \frac{1}{x^{3}}y^{-2}$$

Multiply 4 times 2.

$$8\times \frac{1}{x^{3}}\times \frac{1}{y^{2}}$$

Differentiate w.r.t. x

$$-\frac{24}{y^{2}x^{4}}$$