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

Question

.(1 point)
Responses

97
97

2397
23 superscript 97 baseline

133
1 superscript 33 baseline

2333
23 superscript 33 baseline

Answer 1

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

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

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

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

So, the simplified expression is:

\[ 23^{33} \]

Therefore, the correct response is:

2333 (23 superscript 33 baseline).