To simplify the expression $6x^3 \cdot 4x^9$, follow these steps:

1. Multiply the coefficients: $6 \cdot 4 = 24$

2. Apply the property of exponents for multiplication: When multiplying powers with the same base, you add the exponents. $x^3 \cdot x^9 = x^{3+9} = x^{12}$

3. Combine the results: $6x^3 \cdot 4x^9 = 24x^{12}$

So, the simplified expression is: $24x^{12}$

Would you like further details or have any questions about this process?

Here are 5 questions you might want to ask:

1. How do you handle multiplication of terms with the same base?
2. What are the properties of exponents?
3. Can you provide another example of simplifying a similar expression?
4. How do you handle division of terms with the same base?
5. What happens if the exponents are negative or fractional?

Tip: When multiplying terms with the same base, always remember to add the exponents. This rule simplifies the process and helps keep your calculations accurate.