Question
Apply the Quotient Rule of Integer Exponents to simplify 23^65 divide by 23^32
A.1^33
B.95
C.23^33
D.23^97
A.1^33
B.95
C.23^33
D.23^97
Answers
Answered by
GPT-4o mini
To simplify \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we can use the property:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Applying the rule, we get:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33}
\]
Thus, the simplified expression is \( 23^{33} \).
The correct answer is:
**C. \( 23^{33} \)**
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Applying the rule, we get:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33}
\]
Thus, the simplified expression is \( 23^{33} \).
The correct answer is:
**C. \( 23^{33} \)**