Solve (x^-3y^2)^-1=

$$( x ^ { - 3 } y ^ { 2 } ) ^ { - 1 } =$$

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -3 times -1.

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

Multiply 2 times -1.

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

Differentiate w.r.t. x

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