Solve -3x^5y^-71/2x^-3y=

$$-3 { x }^{ 5 } { y }^{ -7 } \frac{ 1 }{ 2 } { x }^{ -3 } y=$$

Evaluate

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

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}x^{5}y^{-7}\times \left(\frac{1}{2}\right)^{1}x^{-3}y^{1}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{5}x^{-3}y^{-7}y^{1}$$

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

$$\left(-3\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{5-3}y^{-7+1}$$

Add the exponents 5 and -3.

$$\left(-3\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{2}y^{-7+1}$$

Add the exponents -7 and 1.

$$\left(-3\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{2}y^{-6}$$

Multiply -3 times \frac{1}{2}.

$$-\frac{3}{2}x^{2}\times \frac{1}{y^{6}}$$

Differentiate w.r.t. x

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