To evaluate the expression \(\left(5^{-1}\right)^{\frac{1}{2}}\), let's go through the steps one by one for clarity:
1. Evaluate the exponent \(5^{-1}\):
[tex]\[
5^{-1}
\][/tex]
When you take a number to the power of \(-1\), you find its reciprocal. Therefore:
[tex]\[
5^{-1} = \frac{1}{5}
\][/tex]
Numerically, \(\frac{1}{5} = 0.2\).
2. Take the square root of \(0.2\):
[tex]\[
\left(\frac{1}{5}\right)^{\frac{1}{2}}
\][/tex]
In mathematical terms, taking the number to the power of \(\frac{1}{2}\) means finding the square root of that number. So, we need to find the square root of \(0.2\).
The square root of \(0.2\) (or \(\frac{1}{5}\)) is approximately:
[tex]\[
\sqrt{0.2} \approx 0.4472135955
\][/tex]
Therefore, the numerical result of the expression \(\left(5^{-1}\right)^{\frac{1}{2}}\) is approximately \(0.4472135955\).
To summarize, the answer is:
[tex]\[
(0.2, 0.4472135954999579)
\][/tex]
