1. **Problem:** Simplify the expression $8x^2 y^3 \cdot 2x^3 y$. 2. **Formula and rules:** When multiplying terms with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$. 3. **Step-by-step solution:** - Multiply the coefficients: $8 \cdot 2 = 16$. - Multiply the $x$ terms: $x^2 \cdot x^3 = x^{2+3} = x^5$. - Multiply the $y$ terms: $y^3 \cdot y^1 = y^{3+1} = y^4$. 4. **Combine all parts:** $$16x^5 y^4$$ 5. **Final answer:** $16x^5 y^4$