Question
Apply the Quotient Rule of Integer Exponents to simplify 23^65 ÷ 23^32
.
options:
23^97
23^33
1^33
97
.
options:
23^97
23^33
1^33
97
Answers
GPT-4o mini
To simplify the expression \( 23^{65} \div 23^{32} \) using the Quotient Rule of Integer Exponents, we apply the rule which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Thus, we have:
\[
23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33}
\]
Therefore, the simplified expression is \( 23^{33} \).
The correct option is:
**23^33**
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Thus, we have:
\[
23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33}
\]
Therefore, the simplified expression is \( 23^{33} \).
The correct option is:
**23^33**