Question
An equation is missing the exponet what is the missing number.
1/81=3^n
1/81=3^n
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( \frac{1}{81} = 3^n \), we first rewrite \( \frac{1}{81} \) as a power of 3.
Since \( 81 = 3^4 \), we can express \( \frac{1}{81} \) as:
\[
\frac{1}{81} = \frac{1}{3^4} = 3^{-4}
\]
Now, we can set the two sides equal to each other:
\[
3^{-4} = 3^n
\]
Since the bases are the same, we can equate the exponents:
\[
n = -4
\]
Thus, the missing exponent \( n \) is \(-4\).
Since \( 81 = 3^4 \), we can express \( \frac{1}{81} \) as:
\[
\frac{1}{81} = \frac{1}{3^4} = 3^{-4}
\]
Now, we can set the two sides equal to each other:
\[
3^{-4} = 3^n
\]
Since the bases are the same, we can equate the exponents:
\[
n = -4
\]
Thus, the missing exponent \( n \) is \(-4\).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.