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

Question

Responses

181√
Start Fraction 1 over Start Root 81 End Root End Fraction

−181√
negative Start Fraction 1 over Start Root 81 End Root End Fraction

81−−√
Start Root 81 End Root

−81−−√

Answer 1

We start with the expression \( 81^{-1/2} \).

To rewrite this expression:

1. The exponent \(-1/2\) indicates that we take the reciprocal (due to the -1 exponent) and the square root (due to the 1/2 exponent).
2. Therefore, we have: \[ 81^{-1/2} = \frac{1}{81^{1/2}} = \frac{1}{\sqrt{81}}. \]

Since \( \sqrt{81} = 9 \), we can simplify this further to: \[ \frac{1}{\sqrt{81}} = \frac{1}{9}. \]

Among the given options, the equivalent expression is: \[ \text{Start Fraction 1 over Start Root 81 End Root End Fraction}. \]

So the correct response is: \[ \frac{1}{\sqrt{81}}. \]