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Original Question
Find the numerical equivalent of 9^9 * 9^-6Question
Find the numerical equivalent of 3^9 . 3^-5
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Answered by
GPT-4o mini
To find the numerical equivalent of \( 3^9 \cdot 3^{-5} \), we can use the property of exponents that states:
\[
a^m \cdot a^n = a^{m+n}
\]
Applying this property, we have:
\[
3^9 \cdot 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^4
\]
Now, we can calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Thus, the numerical equivalent of \( 3^9 \cdot 3^{-5} \) is \( \boxed{81} \).
\[
a^m \cdot a^n = a^{m+n}
\]
Applying this property, we have:
\[
3^9 \cdot 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^4
\]
Now, we can calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Thus, the numerical equivalent of \( 3^9 \cdot 3^{-5} \) is \( \boxed{81} \).
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