To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we first need to understand that the square root can be expressed as a fractional exponent. The square root of a number can be rewritten as raising that number to the power of \( \frac{1}{2} \).
Thus, we can rewrite \( \sqrt{3} \) as \( 3^{1/2} \). However, since the original expression is \( 5 - \sqrt{3} \), we focus only on rewriting \( \sqrt{3} \).
The expression \( 5 - \sqrt{3} \) doesn't lend itself to rewriting as a single term with a rational exponent. The options provided are more indicative of either a misunderstanding of what you are trying to achieve or a misinterpretation.
Therefore, from the options given, the correct way to express just the \( \sqrt{3} \) part in rational exponent form would be:
5 - 3^{1/2}
However, since that's not one of the answers provided, I cannot select from the options listed. If you specifically wanted to rewrite only \( \sqrt{3} \), the correct form of a root using a rational exponent on its own would be \( 3^{1/2} \), but since it's not an option we can select, we need clarification on the intent of the problem.
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