1. **State the problem:** Simplify the expression $$(2x^3 y^4)^5$$ and express the answer with positive exponents. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power: $$ (ab)^n = a^n b^n $$ 3. **Apply the rule:** $$ (2x^3 y^4)^5 = 2^5 (x^3)^5 (y^4)^5 $$ 4. **Simplify each term:** $$ 2^5 = 32 $$ $$ (x^3)^5 = x^{3 \times 5} = x^{15} $$ $$ (y^4)^5 = y^{4 \times 5} = y^{20} $$ 5. **Combine all parts:** $$ 32 x^{15} y^{20} $$ 6. **Final answer:** $$ \boxed{32 x^{15} y^{20}} $$