Apply the Quotient Rule of Integer Exponents to simplify 23^65 divide by 23^32

Question

A.1^33
B.95
C.23^33
D.23^97

Answer 1

To simplify \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we can use the property:

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

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

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

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

The correct answer is:

C. \( 23^{33} \)