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 ${81}^{-12}$.