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Answer :
To evaluate the expression [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex], let's break it down step-by-step:
1. Understand [tex]\(5^{-1}\)[/tex]:
- The expression [tex]\(5^{-1}\)[/tex] represents [tex]\( \frac{1}{5} \)[/tex]. This is because any number raised to the power of -1 is equal to the reciprocal of that number.
2. Evaluate [tex]\(\left(\frac{1}{5}\right)^{\frac{1}{2}}\)[/tex]:
- When you raise a number to the power of [tex]\(\frac{1}{2}\)[/tex], you are finding the square root of that number.
3. Find the square root:
- The square root of [tex]\(\frac{1}{5}\)[/tex] is approximately 0.4472.
Now, let's match this result with the options provided. Since 0.4472 is not exactly any of the options listed nor can it be a direct expression as a fraction, it tells us the exact result isn't a simple fraction like those given.
However, none of the provided answer choices match the numeric result of approximately 0.4472. But, if we think in terms of fractions, this value is close to [tex]\(\frac{1}{\sqrt{25}}\)[/tex] because [tex]\(\sqrt{25} = 5\)[/tex], you might expect a fraction form to approximately match the behavior of a square root process in fractional powers, leading us to:
- The correct divisor and setup aren't available as perfect matches because [tex]\(\frac{1}{5}\)[/tex] doesn't resolve directly to a known fractional form like those that include [tex]\( \pm 25 \)[/tex].
The result of [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] is approximately 0.4472, which corresponds more closely to an expression using radical or decimal approximation rather than a precise simplistic fraction presented in the options. The expression accurately captures the rule for combining negative reciprocal and half powers, expressing the transformation and steps evaluated.
1. Understand [tex]\(5^{-1}\)[/tex]:
- The expression [tex]\(5^{-1}\)[/tex] represents [tex]\( \frac{1}{5} \)[/tex]. This is because any number raised to the power of -1 is equal to the reciprocal of that number.
2. Evaluate [tex]\(\left(\frac{1}{5}\right)^{\frac{1}{2}}\)[/tex]:
- When you raise a number to the power of [tex]\(\frac{1}{2}\)[/tex], you are finding the square root of that number.
3. Find the square root:
- The square root of [tex]\(\frac{1}{5}\)[/tex] is approximately 0.4472.
Now, let's match this result with the options provided. Since 0.4472 is not exactly any of the options listed nor can it be a direct expression as a fraction, it tells us the exact result isn't a simple fraction like those given.
However, none of the provided answer choices match the numeric result of approximately 0.4472. But, if we think in terms of fractions, this value is close to [tex]\(\frac{1}{\sqrt{25}}\)[/tex] because [tex]\(\sqrt{25} = 5\)[/tex], you might expect a fraction form to approximately match the behavior of a square root process in fractional powers, leading us to:
- The correct divisor and setup aren't available as perfect matches because [tex]\(\frac{1}{5}\)[/tex] doesn't resolve directly to a known fractional form like those that include [tex]\( \pm 25 \)[/tex].
The result of [tex]\(\left(5^{-1}\right)^{\frac{1}{2}}\)[/tex] is approximately 0.4472, which corresponds more closely to an expression using radical or decimal approximation rather than a precise simplistic fraction presented in the options. The expression accurately captures the rule for combining negative reciprocal and half powers, expressing the transformation and steps evaluated.
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