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The value that fills the square is **-3**.
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The Deep Dive
To solve for \( \square \), we can rewrite the equation \( \frac{1}{a^{3}} = a^{\square} \). This is equivalent to saying that \( a^{\square} = a^{-3} \), since \( \frac{1}{a^{3}} \) can be expressed as \( a^{-3} \). Since the bases are the same, we can equate the exponents. Therefore, we have: \[ \square = -3. \] In summary, the value for \( \square \) is \(-3\).
