Question

According to exponent rules, what is the rational exponent in the equivalent expression to 5–√3
? Enter your response in fraction form.(1 point)
$$
Incorrect

The index of the radicand gives key information when generating a rational exponent.

Answer 1

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.