Question

Which of the following is an equivalent expression to 81^− 1/2?(1 point)
Responses

-√81

− 1/√81

√81

1/√81

Answer 1

To simplify \( 81^{-1/2} \), we can apply the rules of exponents.

The expression \( 81^{-1/2} \) can be rewritten as:

\[
\frac{1}{81^{1/2}}
\]

Since \( 81^{1/2} \) is the square root of 81, we have:

\[
81^{1/2} = \sqrt{81}
\]

Thus, we can write:

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

Now, we can evaluate:

\[
\sqrt{81} = 9
\]

So,

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

From the options given, the expression \( \frac{1}{\sqrt{81}} \) is the equivalent expression we derived.

Therefore, the correct response is:

**1/√81**