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Answer :
To evaluate the expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex], let's break it down into steps:
1. Evaluate [tex]\(5^{-1}\)[/tex]:
- The expression [tex]\(5^{-1}\)[/tex] means the reciprocal of 5, which is [tex]\(\frac{1}{5}\)[/tex].
2. Take the square root of [tex]\(\frac{1}{5}\)[/tex]:
- The expression [tex]\(\left(\frac{1}{5}\right)^{\frac{1}{2}}\)[/tex] means the square root of [tex]\(\frac{1}{5}\)[/tex].
- Taking the square root of a fraction involves taking the square root of the numerator and the square root of the denominator separately.
- The square root of 1 is 1, and the square root of 5 is [tex]\(\sqrt{5}\)[/tex].
- Therefore, the result is [tex]\(\frac{1}{\sqrt{5}}\)[/tex].
To put this in a multiple-choice context, since [tex]\(\frac{1}{\sqrt{5}}\)[/tex] is approximately 0.447, the numerical expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] evaluates to [tex]\(\frac{1}{\sqrt{5}}\)[/tex], which is closest to the option [tex]\( \frac{1}{25} \)[/tex].
So, the correct answer is:
[tex]\(\frac{1}{25}\)[/tex]
1. Evaluate [tex]\(5^{-1}\)[/tex]:
- The expression [tex]\(5^{-1}\)[/tex] means the reciprocal of 5, which is [tex]\(\frac{1}{5}\)[/tex].
2. Take the square root of [tex]\(\frac{1}{5}\)[/tex]:
- The expression [tex]\(\left(\frac{1}{5}\right)^{\frac{1}{2}}\)[/tex] means the square root of [tex]\(\frac{1}{5}\)[/tex].
- Taking the square root of a fraction involves taking the square root of the numerator and the square root of the denominator separately.
- The square root of 1 is 1, and the square root of 5 is [tex]\(\sqrt{5}\)[/tex].
- Therefore, the result is [tex]\(\frac{1}{\sqrt{5}}\)[/tex].
To put this in a multiple-choice context, since [tex]\(\frac{1}{\sqrt{5}}\)[/tex] is approximately 0.447, the numerical expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] evaluates to [tex]\(\frac{1}{\sqrt{5}}\)[/tex], which is closest to the option [tex]\( \frac{1}{25} \)[/tex].
So, the correct answer is:
[tex]\(\frac{1}{25}\)[/tex]
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