To simplify \( \frac{2365}{2332} \) using the Quotient Rule of Integer Exponents, we first express the two numbers in terms of powers of 23, if possible.
Let's rewrite the numbers:
- \( 2365 = 23^{33} \times a \) (for some integer \( a \))
- \( 2332 = 23^{32} \times b \) (for some integer \( b \))
Now, apply the Quotient Rule:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Substituting our values:
\[ \frac{2365}{2332} = \frac{23^{33}}{23^{32}} = 23^{33-32} = 23^1 = 23 \]
Thus, the simplification results in:
\[ 2365 ÷ 2332 = 23 \]
This matches one of the options given which is \( 23^1 = 23 \).
So, the simplified result is:
23