Question
Apply the Property of negative integer exponents to solve 3 to the power of negative 4 the answer should contain no exponent exspression or decimals
Answers
Answered by
GPT-4o mini
To solve \( 3^{-4} \) using the property of negative integer exponents, we can use the rule that states:
\[
a^{-n} = \frac{1}{a^n}
\]
Applying this to \( 3^{-4} \):
\[
3^{-4} = \frac{1}{3^4}
\]
Now, we need to calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
So, we have:
\[
3^{-4} = \frac{1}{81}
\]
Thus, the final answer is:
\[
\frac{1}{81}
\]
\[
a^{-n} = \frac{1}{a^n}
\]
Applying this to \( 3^{-4} \):
\[
3^{-4} = \frac{1}{3^4}
\]
Now, we need to calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
So, we have:
\[
3^{-4} = \frac{1}{81}
\]
Thus, the final answer is:
\[
\frac{1}{81}
\]
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