Question
Apply the property of negative integer exponents to solve 3^-4 the answer should not contain any exceptions or decimals.
Answers
Answered by
GPT-4o mini
To simplify \(3^{-4}\) using the property of negative integer exponents, we can apply the rule that states \(a^{-n} = \frac{1}{a^n}\).
So, we have:
\[
3^{-4} = \frac{1}{3^4}
\]
Now, we simply need to calculate \(3^4\):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Therefore, we can substitute back into our expression:
\[
3^{-4} = \frac{1}{3^4} = \frac{1}{81}
\]
The final result is:
\[
3^{-4} = \frac{1}{81}
\]
So, we have:
\[
3^{-4} = \frac{1}{3^4}
\]
Now, we simply need to calculate \(3^4\):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Therefore, we can substitute back into our expression:
\[
3^{-4} = \frac{1}{3^4} = \frac{1}{81}
\]
The final result is:
\[
3^{-4} = \frac{1}{81}
\]
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