To simplify the expression [tex]\((3x^3)(4x^4)\)[/tex], we need to follow these steps:
1. Multiply the coefficients: The coefficients are the numerical parts of the terms. In this case, we have 3 and 4.
[tex]\[
3 \times 4 = 12
\][/tex]
2. Add the exponents of [tex]\(x\)[/tex]: When multiplying terms with the same base (in this case, [tex]\(x\)[/tex]), we add their exponents. The exponents we have are 3 and 4.
[tex]\[
3 + 4 = 7
\][/tex]
3. Combine the results: The new term will have the coefficient resulting from the multiplication and the exponent resulting from the addition.
[tex]\[
12x^7
\][/tex]
So, the simplified expression is:
[tex]\[
12 x^7
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{12 x^7}
\][/tex]
