To solve $81^{\frac{3}{4}}$, follow these steps:

1. Rewrite the base:
   $81 = 3^4$ (since $81 = 3 \times 3 \times 3 \times 3$).

2. Apply the exponent rule:
   Using the rule $(a^m)^n = a^{m \cdot n}$, we rewrite the expression: $81^{\frac{3}{4}} = (3^4)^{\frac{3}{4}} = 3^{4 \cdot \frac{3}{4}} = 3^3.$

3. Simplify:
   Now calculate $3^3$: [ 3^3 = 3 \times 3 \times