Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332

Question

.(1 point)
Responses

2397
23 superscript 97 baseline

133
1 superscript 33 baseline

97
97

2333

Answer 1

To simplify \( 2365 \div 2332 \) using the Quotient Rule of Integer Exponents, we start by applying the rule which states:

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

In this case, we can rewrite \( 2365 \) and \( 2332 \) as \( 23^{65} \) and \( 23^{32} \) respectively:

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

Thus, the simplified expression is:

\[ 23^{33} \]

The correct response is:

1 superscript 33 baseline