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

1^33
23^97
97
23^33

1 answer

To simplify \( \frac{2365}{2332} \) using the Quotient Rule of Integer Exponents, we first express the two numbers in terms of powers of 23, if possible.

Let's rewrite the numbers:

  • \( 2365 = 23^{33} \times a \) (for some integer \( a \))
  • \( 2332 = 23^{32} \times b \) (for some integer \( b \))

Now, apply the Quotient Rule:

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

Substituting our values:

\[ \frac{2365}{2332} = \frac{23^{33}}{23^{32}} = 23^{33-32} = 23^1 = 23 \]

Thus, the simplification results in:

\[ 2365 ÷ 2332 = 23 \]

This matches one of the options given which is \( 23^1 = 23 \).

So, the simplified result is:

23