√(-а) ²•(а-²)²

To simplify the expression \( \sqrt{-a}^2 \cdot (a^{-2})^2 \), we can break it down step by step: 1. **Simplify \( \sqrt{-a}^2 \)**: \[ \sqrt{-a}^2 = -a \] (Note that \( \sqrt{x}^2 \) gives \( x \) if \( x \) is non-negative, but here we consider it in the context of complex numbers, where \( \sqrt{-a} \) could be defined.) 2. **Simplify \( (a^{-2})^2 \)**: \[ (a^{-2})^2 = a^{-4} \] 3. **Combine the results**: Now, we multiply the results: \[ -a \cdot a^{-4} = -a^{1} \cdot a^{-4} = -a^{1-4} = -a^{-3} \] Thus, the simplified result of the expression \( \sqrt{-a}^2 \cdot (a^{-2})^2 \) is: \[ -a^{-3} \] Alternatively, it can also be expressed as: \[ -\frac{1}{a^3} \quad \text{(if \( a \neq 0 \))} \]