Apply the Quotient Rule of Integer Exponents to simplify 23(65) ÷ 23(32)

Question

.(1 point)
Responses

97
97

23(97)
23 superscript 97 baseline

1(33)
1 superscript 33 baseline

23(33)

Answer 1

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

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

In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Applying the rule:

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

So, the simplified expression is \( 23^{33} \).

The correct response is:

\( 23^{33} \)