Apply the Quotient Rule of Integer Exponents to simplify 23 raised to the power of 65 ÷ 23 raised to the power of 32 .

Answer 1

To simplify \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we use the rule which states:

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

In this case, we have:

• \( a = 23 \)
• \( m = 65 \)
• \( n = 32 \)

Applying the rule:

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

Now, we calculate \( 65 - 32 \):

\[ 65 - 32 = 33 \]

Thus, we have:

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

Therefore, the simplified expression is:

\[ \boxed{23^{33}} \]