Solve for y y^0+y^1=1/(x^-2)

$y^{0} + y^{1} = \frac{1}{x^{- 2}}$

Simplify each term.

Anything raised to $0$ is $1$ .

$1 + y^{1} = \frac{1}{x^{- 2}}$

Simplify.

$1 + y = \frac{1}{x^{- 2}}$

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$1 + y = x^{2}$

Subtract $1$ from both sides of the equation.

$y = x^{2} - 1$