Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332 .(1 point) Responses 133 1 superscript 33 baseline 97 97 2397 23 superscript 97 baseline 2333

1 answer

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

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

First, we need to rewrite the numbers in the expression in terms of powers of 23, since both numbers appear to have the base of 23:

  • \( 2365 = 23^{65} \)
  • \( 2332 = 23^{32} \)

Now we can apply the quotient rule:

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

So the simplified expression is:

\[ 23^{33} \]

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