To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we need to focus on the square root and how it relates to rational exponents. The square root of a number can be expressed with a rational exponent as follows:
\[ \sqrt{a} = a^{\frac{1}{2}} \]
However, the expression \( 5 - \sqrt{3} \) itself doesn't directly translate into a rational exponent only for the square root. If we were to focus solely on the square root component, we could write:
\[ \sqrt{3} = 3^{\frac{1}{2}} \]
But since the whole expression \( 5 - \sqrt{3} \) is being asked to be rewritten, it seems there might be a misunderstanding about changing expressions directly including negative signs or basic arithmetic.
From the responses you provided, none of them directly relate to the use of a rational exponent in the context of a subtraction in the original expression.
Please clarify if you're specifically looking to express just the square root term (like \( \sqrt{3} \)) or otherwise specify another related expression. If it’s the root specifically:
\( \sqrt{3} = 3^{\frac{1}{2}} \)
If focusing on rewriting as a whole, we can't correctly transform \( 5 - \sqrt{3} \) into a simple rational exponent without context.
So the answer regarding how to express the square root term is:
3^{\frac{1}{2}}
If we are restructuring the whole expression, the mathematical representation may remain as is unless stated otherwise.
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