Solve (8x^4y^-3)(1/2x^-5y^2)

$$( 8 x ^ { 4 } y ^ { - 3 } ) ( \frac { 1 } { 2 } x ^ { - 5 } y ^ { 2 } )$$

Evaluate

$$\frac{4}{xy}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$8^{1}x^{4}y^{-3}\times \left(\frac{1}{2}\right)^{1}x^{-5}y^{2}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \left(\frac{1}{2}\right)^{1}x^{4}x^{-5}y^{-3}y^{2}$$

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

$$8^{1}\times \left(\frac{1}{2}\right)^{1}x^{4-5}y^{-3+2}$$

Add the exponents 4 and -5.

$$8^{1}\times \left(\frac{1}{2}\right)^{1}\times \frac{1}{x}y^{-3+2}$$

Add the exponents -3 and 2.

$$8^{1}\times \left(\frac{1}{2}\right)^{1}\times \frac{1}{x}\times \frac{1}{y}$$

Multiply 8 times \frac{1}{2}.

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

Differentiate w.r.t. x

$$-\frac{4}{yx^{2}}$$