Which of the following is an equivalent expression to 81−12

Question

?(1 point)
Responses

−81−−√
negative Start Root 81 End Root

81−−√
Start Root 81 End Root

181√
Start Fraction 1 over Start Root 81 End Root End Fraction

−181√

Answer 1

To find an equivalent expression to \( 81^{-12} \), let's first rewrite it in a more manageable form.

The expression \( 81^{-12} \) can be expressed as:

\[ \frac{1}{81^{12}} \]

Next, we also know that \( 81 \) can be written as \( 3^4 \). Therefore, we can rewrite \( 81^{12} \) as follows:

\[ 81^{12} = (3^4)^{12} = 3^{4 \cdot 12} = 3^{48} \]

Thus, we can express \( 81^{-12} \) as:

\[ 81^{-12} = \frac{1}{81^{12}} = \frac{1}{3^{48}} \]

Now let’s analyze the options provided:

1. \( -\sqrt{81} \): This evaluates to \(-9\), not equivalent.
2. \( \sqrt{81} \): This evaluates to \(9\), not equivalent.
3. \( \frac{1}{\sqrt{81}} \): This evaluates to \(\frac{1}{9}\), not equivalent.
4. \( -\frac{1}{\sqrt{81}} \): This evaluates to \(-\frac{1}{9}\), not equivalent.

None of the options given appears to be a direct equivalent expression to \( 81^{-12} \) or \(\frac{1}{81^{12}}\).

If any of the options may have typographical errors, please re-check or clarify, but based on the given expressions, none is equivalent to \( 81^{-12} \).