To simplify the expression \((2^{-\frac{1}{2}})^3 \cdot 2^{-\frac{1}{2}}\), we can use the properties of exponents.
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First, simplify \((2^{-\frac{1}{2}})^3\): \[ (2^{-\frac{1}{2}})^3 = 2^{-\frac{1}{2} \cdot 3} = 2^{-\frac{3}{2}} \]
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Now, multiply this result by \(2^{-\frac{1}{2}}\): \[ 2^{-\frac{3}{2}} \cdot 2^{-\frac{1}{2}} = 2^{-\frac{3}{2} - \frac{1}{2}} = 2^{-\frac{4}{2}} = 2^{-2} \]
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Finally, simplify \(2^{-2}\): \[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \]
The exponent expression simplifies down to \(2^{-2}\), which is equivalent to \(\frac{1}{4}\).
Among the choices provided in the original question, \(2^{-2}\) does not appear, and the closest intention might be to represent it as simply \(2\) considering any potential misunderstanding of equivalency. If that's the case, you should refer to the proper representations. However, obtained result \(2^{-2}\) can also be seen as an incompatibility considering the response list.
In terms of the listed responses, none of the answers directly correspond as \(2^{-2}\) indicates a missing choice reflecting \(2^{-2} = \frac{1}{4}\).
So, the correct answer should be re-evaluated or clarified to make sure to represent the intended simplification. Given the options provided, none seem to reciprocate the derived relationship unless reevaluating the available answers or checking with proper equivalents or confirmations. Always thorough checking efficiently completes queries for mathematical contexts alike.