Apply the quotient rule of integers exponents to simplify 23^65 divided by 23^32

Answer 1

To simplify the expression \( \frac{23^{65}}{23^{32}} \) using the quotient rule of integer exponents, you can subtract the exponents of the same base. The quotient rule states that:

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

Here, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Applying the rule, we get:

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

Now, perform the subtraction in the exponent:

\[ 65 - 32 = 33 \]

Thus, the simplified expression is:

\[ 23^{33} \]