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Answer :
Sure! Let's evaluate the expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] step by step.
1. Understand the expression: The expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] can be broken down into two operations. First, we deal with [tex]\(5^{-1}\)[/tex], and then we raise that result to the power of [tex]\(\frac{1}{2}\)[/tex].
2. Calculate [tex]\(5^{-1}\)[/tex]: The notation [tex]\(5^{-1}\)[/tex] represents the reciprocal of 5, which is:
[tex]\[
5^{-1} = \frac{1}{5}
\][/tex]
3. Raise to the power of [tex]\(\frac{1}{2}\)[/tex]: Next, we need to raise [tex]\(\frac{1}{5}\)[/tex] to the power of [tex]\(\frac{1}{2}\)[/tex], which is equivalent to finding the square root of [tex]\(\frac{1}{5}\)[/tex].
4. Calculate the square root of [tex]\(\frac{1}{5}\)[/tex]: The square root of [tex]\(\frac{1}{5}\)[/tex] is approximately 0.4472.
So, the final result of [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] is approximately 0.4472. This does not correspond exactly to any of the options provided (25, -25, [tex]\(\frac{1}{25}\)[/tex], [tex]\(-\frac{1}{25}\)[/tex]), but the numerical result indicates that the expression evaluates to about 0.4472.
1. Understand the expression: The expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] can be broken down into two operations. First, we deal with [tex]\(5^{-1}\)[/tex], and then we raise that result to the power of [tex]\(\frac{1}{2}\)[/tex].
2. Calculate [tex]\(5^{-1}\)[/tex]: The notation [tex]\(5^{-1}\)[/tex] represents the reciprocal of 5, which is:
[tex]\[
5^{-1} = \frac{1}{5}
\][/tex]
3. Raise to the power of [tex]\(\frac{1}{2}\)[/tex]: Next, we need to raise [tex]\(\frac{1}{5}\)[/tex] to the power of [tex]\(\frac{1}{2}\)[/tex], which is equivalent to finding the square root of [tex]\(\frac{1}{5}\)[/tex].
4. Calculate the square root of [tex]\(\frac{1}{5}\)[/tex]: The square root of [tex]\(\frac{1}{5}\)[/tex] is approximately 0.4472.
So, the final result of [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] is approximately 0.4472. This does not correspond exactly to any of the options provided (25, -25, [tex]\(\frac{1}{25}\)[/tex], [tex]\(-\frac{1}{25}\)[/tex]), but the numerical result indicates that the expression evaluates to about 0.4472.
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