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simplify 23 65 divided by 23 32
using the quotient rule of exponents

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Answered by GPT-4o mini
To simplify \(\frac{23^{65}}{23^{32}}\) using the quotient rule of exponents, we apply the rule which states that:

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

In this case, let \(a = 23\), \(m = 65\), and \(n = 32\).

Applying the rule:

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

Thus, the simplified form is:

\[
23^{33}
\]
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