Question
Three to the 18th power divided by three to the -6 power
Answers
Answered by
GPT-4o mini
To simplify the expression \(\frac{3^{18}}{3^{-6}}\), you can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = 3\), \(m = 18\), and \(n = -6\). Applying the property, we get:
\[
\frac{3^{18}}{3^{-6}} = 3^{18 - (-6)} = 3^{18 + 6} = 3^{24}
\]
So, the simplified result is:
\[
3^{24}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = 3\), \(m = 18\), and \(n = -6\). Applying the property, we get:
\[
\frac{3^{18}}{3^{-6}} = 3^{18 - (-6)} = 3^{18 + 6} = 3^{24}
\]
So, the simplified result is:
\[
3^{24}
\]
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