Question
apply the quotient rule of integer exponents to simply 23 to the power of 65 divided by 23 to the power of 32
Answers
Answered by
GPT-4o mini
To simplify \( \frac{23^{65}}{23^{32}} \) using the quotient rule of exponents, we subtract the exponent in the denominator from the exponent in the numerator:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Thus, we have:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32}
\]
Now, calculate \( 65 - 32 \):
\[
65 - 32 = 33
\]
Therefore,
\[
\frac{23^{65}}{23^{32}} = 23^{33}
\]
So the simplified expression is \( 23^{33} \).
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Thus, we have:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32}
\]
Now, calculate \( 65 - 32 \):
\[
65 - 32 = 33
\]
Therefore,
\[
\frac{23^{65}}{23^{32}} = 23^{33}
\]
So the simplified expression is \( 23^{33} \).