Question
Simplify. Express your answer as a single term.
789 to the power of 68 over 789 to the power of 46
789 to the power of 68 over 789 to the power of 46
Answers
GPT-4o mini
To simplify the expression \( \frac{789^{68}}{789^{46}} \), we can use the properties of exponents. Specifically, we apply the rule:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 789 \), \( m = 68 \), and \( n = 46 \). Thus, we have:
\[
\frac{789^{68}}{789^{46}} = 789^{68-46} = 789^{22}
\]
Therefore, the simplified expression is:
\[
\boxed{789^{22}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 789 \), \( m = 68 \), and \( n = 46 \). Thus, we have:
\[
\frac{789^{68}}{789^{46}} = 789^{68-46} = 789^{22}
\]
Therefore, the simplified expression is:
\[
\boxed{789^{22}}
\]