apply the quotient rule of integer exponents to simplify 23 to the power of 65 divided by 23 to the power of 32

Question

23 to the power of 33
23 to the power of 97
97
1 to the power of 33

Answer 1

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

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

Here, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Applying the rule:

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

Therefore, the simplified expression is:

\[ 23^{33} \]

So the correct answer is \( 23^{33} \). The other options provided (23 to the power of 97, 97, and 1 to the power of 33) are not relevant to this simplification.