To solve for \( y \) in the equation \( y^{-2} = x \), follow these steps:

1. Start with the given equation:
   \[
   y^{-2} = x
   \]
2. To eliminate the negative exponent, take the reciprocal of both sides:
   \[
   \frac{1}{y^2} = x
   \]
3. Now, multiply both sides by \( y^2 \) to get rid of the fraction:
   \[
   1 = x \cdot y^2
   \]
4. Divide both sides by \( x \):
   \[
   y^2 = \frac{1}{x}
   \]
5. Finally, take the square root of both sides to solve for \( y \):
   \[
   y = \pm \frac{1}{\sqrt{x}}
   \]

Thus, the solution is:
\[
y = \pm \frac{1}{\sqrt{x}}
\]

Would you like more details or have any questions?

Here are some related questions:
1. What is the domain of the function \( y = \frac{1}{\sqrt{x}} \)?
2. How does the behavior of \( y^{-n} = x \) change as \( n \) increases?
3. What is the solution if \( y^{-3} = x \)?
4. How does the sign of \( x \) affect the solution in this case?
5. What if the original equation was \( y^{-2} = -x \)?

**Tip**: When solving for a variable with a negative exponent, try eliminating the negative exponent by taking the reciprocal first!

Learn how to solve the equation y^-2 = x by clearing y using exponent rules and square roots. This step-by-step guide covers essential algebraic concepts including exponents, reciprocals, and radicals, making it suitable for students in Grades 9-11.

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