Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332 .(1 point)

Responses

133
1 superscript 33 baseline

2333
23 superscript 33 baseline

97
97

2397

1 answer

To simplify \( \frac{2365}{2332} \) using the Quotient Rule of Integer Exponents, we use the rule:

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

In this case, we can express 2365 and 2332 as powers of 23:

\[ 2365 = 23^{65} \quad \text{and} \quad 2332 = 23^{32} \]

Thus, we can rewrite the expression as:

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

The simplified expression is:

\[ 23^{33} \]

So the correct response is:

23 superscript 33 baseline