Answer :
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]
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]
