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

Simplify the expression by following steps: - step0: Solution: \(\left(x^{2}y^{-2}\right)^{-1}\) - step1: Use the properties of exponents: \(\left(x^{2}\right)^{-1}\left(y^{-2}\right)^{-1}\) - step2: Evaluate the power: \(x^{-2}y^{2}\) - step3: Simplify: \(\frac{y^{2}}{x^{2}}\) To simplify the expression \( \left(x^{2} y^{-2}\right)^{-1} \), we can follow these steps: 1. **Apply the negative exponent rule**: The rule states that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite the expression as: \[ \left(x^{2} y^{-2}\right)^{-1} = \frac{1}{x^{2} y^{-2}} \] 2. **Simplify the denominator**: The term \( y^{-2} \) can be rewritten as \( \frac{1}{y^{2}} \). Thus, we have: \[ x^{2} y^{-2} = x^{2} \cdot \frac{1}{y^{2}} = \frac{x^{2}}{y^{2}} \] 3. **Substituting back into the expression**: Now we can substitute this back into our expression: \[ \frac{1}{x^{2} y^{-2}} = \frac{1}{\frac{x^{2}}{y^{2}}} = \frac{y^{2}}{x^{2}} \] Thus, the simplified form of \( \left(x^{2} y^{-2}\right)^{-1} \) is: \[ \frac{y^{2}}{x^{2}} \]