Question
Apply the Quotient Rule of Integer Exponents to simplify 23 raised to the power of 65÷23 raised to the power of 32 .
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we can apply the rule, which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In our case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Therefore, we can rewrite the expression as follows:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32}
\]
Now, we perform the subtraction in the exponent:
\[
65 - 32 = 33
\]
So, we have:
\[
\frac{23^{65}}{23^{32}} = 23^{33}
\]
Thus, the simplified result is:
\[
23^{33}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In our case, \( a = 23 \), \( m = 65 \), and \( n = 32 \). Therefore, we can rewrite the expression as follows:
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32}
\]
Now, we perform the subtraction in the exponent:
\[
65 - 32 = 33
\]
So, we have:
\[
\frac{23^{65}}{23^{32}} = 23^{33}
\]
Thus, the simplified result is:
\[
23^{33}
\]