To simplify the expression \((3^{-4})^4\), we need to use the power of a power property, which states that \((a^b)^c = a^{bc}\).
So, applying this property to our expression, we have:
\((3^{-4})^4 = 3^{-4\times 4} = 3^{-16}\).
To further simplify, we can use the definition of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\). Applying this definition to our expression:
\(3^{-16} = \frac{1}{3^{16}}\).
Therefore, \((3^{-4})^4\) simplifies to \(\frac{1}{3^{16}}\).
(3^-4)^4
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