To simplify the expression \( 4^4 \times (4^{-2})^4 \), we can use the properties of exponents.
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We start with the expression: \[ 4^4 \times (4^{-2})^4 \]
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We apply the power of a power property, which states that \( (a^m)^n = a^{mn} \): \[ (4^{-2})^4 = 4^{-2 \times 4} = 4^{-8} \]
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Now, our expression becomes: \[ 4^4 \times 4^{-8} \]
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Next, we apply the property of exponents that states \( a^m \times a^n = a^{m+n} \): \[ 4^4 \times 4^{-8} = 4^{4 + (-8)} = 4^{-4} \]
Thus, the expression simplifies to \( 4^{-4} \).
Therefore, the correct answer from the multiple choice options is: \[ \boxed{4^{-4}} \]