Question

Apply the Quotient Rule of Integer Exponents to simplify  23 with the exponent 65 divided by 23 with an exponent of 32 .(1 point) Responses 23 with the exponent of 33, 97, 1 with the exponent of 33, 23 with the exponent 97.

Answer 1

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

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

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

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

So the simplified result is \( 23^{33} \).

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