1. **State the problem:** Simplify the expression $$(3^7)^3$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$ 3. **Apply the rule:** $$ (3^7)^3 = 3^{7 \times 3} $$ 4. **Calculate the exponent:** $$ 7 \times 3 = 21 $$ 5. **Write the simplified expression:** $$ 3^{21} $$ 6. **Final answer:** $$ \boxed{3^{21}} $$