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)
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Incorrect

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

Answer 1

To convert the expression \(5 - \sqrt{3}\) into its equivalent with a rational exponent, we need to focus on the square root part, which is \(\sqrt{3}\).

The square root can be expressed using rational exponents as follows:

\[
\sqrt{3} = 3^{\frac{1}{2}}
\]

Thus, the expression \(5 - \sqrt{3}\) can be rewritten as:

\[
5 - 3^{\frac{1}{2}}
\]

If you are specifically looking for the rational exponent that represents \(\sqrt{3}\), it is \(\frac{1}{2}\).

So, the rational exponent in fractional form is:

\[
\frac{1}{2}
\]