According to exponent rules, what is the rational

The expression \(\sqrt{5^3}\) can be rewritten using the properties of exponents.

The square root can be expressed as an exponent of \(\frac{1}{2}\), so we have:

\[
\sqrt{5^3} = (5^3)^{\frac{1}{2}}.
\]

Now, by using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\), we can simplify this further:

\[
(5^3)^{\frac{1}{2}} = 5^{3 \cdot \frac{1}{2}} = 5^{\frac{3}{2}}.
\]

Thus, the rational exponent in factored form is:

\[
\frac{3}{2} = \frac{3}{1} \cdot \frac{1}{2}.
\]

So, the answer in factored form is:

\[
\frac{3}{1} \cdot \frac{1}{2}.
\]