Solve left(x^2y^-3right)^-1

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times -1.

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

Multiply -3 times -1.

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

Differentiate w.r.t. x

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