1. **Stating the problem:** Find the result of $$\frac{(3^3 p^4)^3}{3 p^2}$$. 2. **Formula and rules:** - Power of a power: $$(a^m)^n = a^{m \times n}$$ - Multiplying powers with the same base: $$a^m \times a^n = a^{m+n}$$ - Dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Step-by-step solution:** - First, simplify the numerator: $$ (3^3 p^4)^3 = 3^{3 \times 3} p^{4 \times 3} = 3^9 p^{12} $$ - Now the expression becomes: $$ \frac{3^9 p^{12}}{3 p^2} $$ - Simplify the division by subtracting exponents of like bases: $$ 3^{9-1} p^{12-2} = 3^8 p^{10} $$ 4. **Final answer:** $$ \boxed{3^8 p^{10}} $$ This is the simplified form of the given expression.