Solve [xy/(x^-3y^-2)^0]=1/x^2

$$[ \frac { x y } { ( x ^ { - 3 } y ^ { - 2 } ) ^ { 0 } } ] = \frac { 1 } { x ^ { 2 } }$$

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$x^{2}xy=1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{3}y=1$$

Divide both sides by x^{3}.

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

Dividing by x^{3} undoes the multiplication by x^{3}.

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

Solve for x (complex solution)

$$x=e^{\frac{2\pi i}{3}}y^{-\frac{1}{3}}$$

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

$$x=e^{\frac{4\pi i}{3}}y^{-\frac{1}{3}}\text{, }y\neq 0$$

Solve for x

$$x=\frac{1}{\sqrt[3]{y}}$$

$$y\neq 0$$