To simplify \( 2365 \div 2332 \) using the Quotient Rule of Integer Exponents, we can express it in terms of powers of 23. The Quotient Rule states that:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Here, we can write:
\[ 2365 = 23^{65} \quad \text{and} \quad 2332 = 23^{32} \]
Now, we can apply the Quotient Rule:
\[ \frac{2365}{2332} = \frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33} \]
Thus, the simplified form of \( 2365 \div 2332 \) is \( 23^{33} \).
From the options provided, the answer is:
2333 (23 superscript 33 baseline).
1 answer