To simplify \( 81^{5/4} \), we start by rewriting 81 as a power of 3:
\[ 81 = 3^4 \]
Now, we can substitute this into our expression:
\[ 81^{5/4} = (3^4)^{5/4} \]
Using the exponent multiplication rule \((a^m)^n = a^{m \cdot n}\):
\[ (3^4)^{5/4} = 3^{4 \cdot (5/4)} \]
Calculating \(4 \cdot (5/4)\):
\[ 4 \cdot \frac{5}{4} = 5 \]
So, we have:
\[ 3^{4 \cdot (5/4)} = 3^5 \]
Next, we calculate \(3^5\):
\[ 3^5 = 243 \]
Thus, the expression \(81^{5/4}\) simplifies to:
\[ \boxed{243} \]