Question

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

1/√81

Answer 2

To simplify the expression \( 81^{-1/2} \), we can interpret the exponent and root:

1. The negative exponent indicates a reciprocal, so \( 81^{-1/2} \) can be rewritten as \( \frac{1}{81^{1/2}} \).
2. The \( 81^{1/2} \) represents the square root of 81, which is 9.

Thus, we get:

\[
81^{-1/2} = \frac{1}{9}
\]

Now let's analyze your options:

1. **\(-81^{-1/2}\)**: This equals \(-\frac{1}{9}\)
2. **\(81^{-1/2}\)**: This equals \(\frac{1}{9}\)
3. **\(\frac{1}{\sqrt{81}}\)**: This equals \(\frac{1}{9}\) (correct equivalence)
4. **\(-\frac{1}{\sqrt{81}}\)**: This equals \(-\frac{1}{9}\)

The equivalent expression to \( 81^{-1/2} \) is:

**\(\frac{1}{\sqrt{81}}\)**.

Answer 3

The expression \( \frac{1}{\sqrt{81}} \) can be simplified:

1. Calculate the square root of 81:
\[
\sqrt{81} = 9
\]

2. Substitute back into the expression:
\[
\frac{1}{\sqrt{81}} = \frac{1}{9}
\]

So, \( \frac{1}{\sqrt{81}} = \frac{1}{9} \).

This confirms that \( \frac{1}{\sqrt{81}} \) is indeed an equivalent expression to \( 81^{-1/2} \).