Question

Which is an equivalent expression to 81^-1/2

Answer 1

Options
1/square root 81
-square root 81
-1/ square root 81
Square root 81

Answer 2

To simplify the expression \( 81^{-1/2} \), we can follow these steps:

1. Recall that \( a^{-b} = \frac{1}{a^b} \). Therefore, we can rewrite \( 81^{-1/2} \) as:
\[
81^{-1/2} = \frac{1}{81^{1/2}}
\]

2. The expression \( 81^{1/2} \) represents the square root of 81. Since \( \sqrt{81} = 9 \), we have:
\[
81^{1/2} = 9
\]

3. Substituting this back into the expression gives:
\[
\frac{1}{81^{1/2}} = \frac{1}{9}
\]

Therefore, the equivalent expression to \( 81^{-1/2} \) is:
\[
\frac{1}{9}
\]

Answer 3

Let's evaluate the options in relation to \( 81^{-1/2} \):

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

From our previous calculation, we found that \( 81^{-1/2} = \frac{1}{9} \), which corresponds to option:

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

Thus, the correct answer is **\( \frac{1}{\sqrt{81}} \)**.