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

Responses

-√81

− 1/√81

√81

1/√81

1 answer

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