To simplify \( 23^{65} \div 23^{32} \) using the quotient rule of integer exponents, we apply the rule which states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). So we have:
\[ 23^{65} \div 23^{32} = 23^{65 - 32} \]
Now, calculate the exponent:
\[ 65 - 32 = 33 \]
Thus, the simplified expression is:
\[ 23^{33} \]
So, \( 23^{65} \div 23^{32} = 23^{33} \).