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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√

3 answers

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:

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

1/√81

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 \( 81^{-1/2} \).