Apply the quotient rule of integer exponents to simplify 23^65 divided by 23^32

Question

A. 1^33
B. 23^97
C. 23^33
D. 97

Answer 1

To simplify \( \frac{23^{65}}{23^{32}} \) using the quotient rule of integer exponents, we apply the rule which states that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). So we calculate:

\[ \frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33} \]

Thus, the simplified form is \( 23^{33} \).

The correct answer is C. \( 23^{33} \).