To convert the expression \(5 - \sqrt{3}\) into a form with a rational exponent, we first need to focus on the square root part \(\sqrt{3}\).
The square root can be expressed with a rational exponent as follows: \[ \sqrt{3} = 3^{1/2} \]
Now, let's address the expression \(5 - \sqrt{3}\). While it contains a whole number (5) and a radical term, the reason you might be looking for a rational exponent can refer specifically to just the \(\sqrt{3}\) part.
Using the rational exponent, \(\sqrt{3}\) is equivalent to \(3^{1/2}\). Therefore, if you are looking specifically for the rational exponent of \(\sqrt{3}\):
The rational exponent is: \[ \frac{1}{2} \]
However, if you're looking for a single rational exponent representing the entire expression \(5 - \sqrt{3}\), it's more complex and cannot be expressed as a single exponent since the subtraction does not directly translate into a rational exponent.
If you're only tasked with finding the rational exponent from \(\sqrt{3}\), it is \(\frac{1}{2}\). If there is a different part of the expression you're supposed to evaluate using rational exponents, please provide additional context.