To simplify the expression \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we can apply the rule, which states that:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In our case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Therefore, we can rewrite the expression as follows:
\[ \frac{23^{65}}{23^{32}} = 23^{65 - 32} \]
Now, we perform the subtraction in the exponent:
\[ 65 - 32 = 33 \]
So, we have:
\[ \frac{23^{65}}{23^{32}} = 23^{33} \]
Thus, the simplified result is:
\[ 23^{33} \]