1. Problem: Simplify the expression $(2x^4y^3)(3x^3y^2)$. 2. Formula: When multiplying terms with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$. 3. Step 1: Multiply the coefficients: $2 \times 3 = 6$. 4. Step 2: Multiply the $x$ terms: $x^4 \cdot x^3 = x^{4+3} = x^7$. 5. Step 3: Multiply the $y$ terms: $y^3 \cdot y^2 = y^{3+2} = y^5$. 6. Final answer: $6x^7y^5$. This uses the property that when multiplying like bases, you add the exponents, and multiply the coefficients normally.