To simplify \( 81^{-\frac{1}{2}} \), we can first rewrite the expression using properties of exponents:
\[ 81^{-\frac{1}{2}} = \frac{1}{81^{\frac{1}{2}}} \]
Now, since \( 81^{\frac{1}{2}} \) is the square root of 81:
\[ 81^{\frac{1}{2}} = \sqrt{81} = 9 \]
Thus,
\[ 81^{-\frac{1}{2}} = \frac{1}{9} \]
Now, let's look at the options you provided:
- \( 1 / (\sqrt{81}) \)
- \( 1 / 9 \)
Since \( \sqrt{81} = 9 \), we have:
\[ 1 / (\sqrt{81}) = 1 / 9 \]
So the equivalent expression is:
Both expressions
So, the expression \( 81^{-\frac{1}{2}} \) is equivalent to \( 1 / ( \sqrt{81} ) \) and \( 1 / 9 \). However, since both simplify to the same value, they are equivalent to \( 81^{-\frac{1}{2}} \).