Question

Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32
23
65
÷
23
32
.(1 point)
Responses

133
1
33
1 superscript 33 baseline

23^33
23
33
23 superscript 33 baseline

97
97

23^97
23
97
23 superscript 97 baseline

Answer 1

To simplify \( 23^{65} \div 23^{32} \) using the Quotient Rule of Integer Exponents, we can apply the rule:

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

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

\[
23^{65} \div 23^{32} = 23^{65-32}
\]

Now, calculate \( 65 - 32 \):

\[
65 - 32 = 33
\]

So,

\[
23^{65} \div 23^{32} = 23^{33}
\]

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

The correct response is:

**23^33**