To simplify \( 81^{-5/4} \), we can first rewrite 81 as a power of a smaller base:
\[ 81 = 3^4 \]
Now substitute \( 81 \) in the expression:
\[ 81^{-5/4} = (3^4)^{-5/4} \]
Using the power of a power property, we multiply the exponents:
\[ (3^4)^{-5/4} = 3^{4 \cdot (-5/4)} = 3^{-5} \]
To express \( 3^{-5} \) in a simpler form, recall that \( a^{-n} = \frac{1}{a^n} \):
\[ 3^{-5} = \frac{1}{3^5} \]
Now, we can compute \( 3^5 \):
\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \]
Therefore,
\[ 81^{-5/4} = \frac{1}{3^5} = \frac{1}{243} \]
The simplified form of \( 81^{-5/4} \) is:
\[ \boxed{\frac{1}{243}} \]