Question

What rational number could be used as an exponent to rewrite 4√23

?(1 point)

Answer 1

The expression \( 4\sqrt{23} \) can be rewritten using rational exponents.

The radical \( \sqrt{23} \) can be expressed as an exponent:

\[
\sqrt{23} = 23^{1/2}
\]

Now, we can rewrite \( 4\sqrt{23} \) as:

\[
4\sqrt{23} = 4 \cdot 23^{1/2}
\]

There is no specific rational number that directly simplifies this expression, but we could express it in terms of a single term if needed. The number \( 4 \) can be expressed as \( 4^{1} \) and written along with \( 23^{1/2} \). However, if you are looking for a single exponent for the term that combines the \( 4 \) and the root aspect together, you might interpret rewriting in a specific context.

If you meant to rewrite just the radical aspect of \( 4\sqrt{23} \), the rational number for \( \frac{1}{2} \) is the exponent for \( \sqrt{23} \).

So, in conclusion, the rational number that can be used as an exponent to rewrite \( \sqrt{23} \) is:

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

If you're combining with \( 4 \) or treating it differently, please clarify the context!