1. **State the problem:** Simplify the expression $10x \times (4x^4) \times (3x^3)$.\n\n2. **Recall the rules:** When multiplying terms with the same base, add the exponents: $x^a \times x^b = x^{a+b}$. Also, multiply the coefficients (numbers) separately.\n\n3. **Multiply the coefficients:** $10 \times 4 \times 3 = 120$.\n\n4. **Multiply the variables:** $x \times x^4 \times x^3 = x^{1+4+3} = x^8$.\n\n5. **Combine the results:** The simplified expression is $120x^8$.