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Answer :
The value of the numerical expression (5^{-4})^{\frac{1}{2}} is \frac{1}{25}. This is found by taking the reciprocal of 5 to the fourth power and then applying the square root.
The numerical expression given is (5^{-4})^{\frac{1}{2}}. To evaluate this, first consider the exponent -4, which means that we are dealing with the reciprocal of 5 raised to the fourth power. That is, 5^{-4} = \frac{1}{5^4} = \frac{1}{625}. Now, to apply the \(\frac{1}{2}\) exponent, also known as the square root, we take the square root of \(\frac{1}{625}\). The square root of 625 is 25, so the square root of \(\frac{1}{625}\) is \(\frac{1}{25}\) since \(\sqrt{\frac{1}{625}} = \frac{1}{\sqrt{625}} = \frac{1}{25}\).
Therefore, the value of the numerical expression (5^{-4})^{\frac{1}{2}} is \frac{1}{25}.
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