To simplify the expression \((2^{-1})^4\), we apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\).
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Using this rule:
\[ (2^{-1})^4 = 2^{-1 \cdot 4} = 2^{-4} \]
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Next, we know that \(2^{-4}\) can be expressed with a positive exponent by using the rule \(a^{-m} = \frac{1}{a^m}\):
\[ 2^{-4} = \frac{1}{2^4} \]
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Now, we calculate \(2^4\):
\[ 2^4 = 16 \]
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Therefore,
\[ 2^{-4} = \frac{1}{16} \]
So, the fully simplified expression without any zero or negative exponents is:
\[ \frac{1}{16} \]
Thus, the answer is:
\(\frac{1}{16}\)