To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we can focus on the term \( \sqrt{3} \). The square root of a number can be expressed as a rational exponent of \( \frac{1}{2} \). Therefore, \( \sqrt{3} \) can be rewritten as \( 3^{1/2} \).
So, we have:
\[ 5 - \sqrt{3} = 5 - 3^{1/2} \]
However, the options provided do not directly relate to this expression. Let's clarify that \( 5 - \sqrt{3} \) does not have a direct rewriting among the choices given (as they focus solely on rational exponents of \( 5 \) and \( 3 \), rather than expressing \( \sqrt{3} \)).
If we are looking solely for how to write \( \sqrt{3} \) using a rational exponent, it is \( 3^{1/2} \). None of the given options are exactly correct for \( 5 - \sqrt{3} \).
If we are just rewriting \( \sqrt{3} \), the correct answer is \( 3^{1/2} \), which isn't listed among your provided responses. If you need an answer based on the provided options, choosing \( 3^{5} \) does not relate to \( \sqrt{3} \) directly. Please verify if the question is about the rational exponent of \( 5 \) or expecting something specific from those choices.
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