To simplify the expression [tex]\((3 x^2)(4 x^3)\)[/tex], we will follow several steps.
### Step 1: Multiply the Coefficients
First, multiply the numerical coefficients (the constants) from each term. Here, the coefficients are 3 and 4.
[tex]\[ 3 \times 4 = 12 \][/tex]
### Step 2: Apply the Laws of Exponents
Next, we need to simplify the variable part of the expression by applying the rules of exponents. When multiplying like bases, we add the exponents.
The terms given are [tex]\( x^2 \)[/tex] and [tex]\( x^3 \)[/tex].
[tex]\[ x^2 \times x^3 = x^{2+3} = x^5 \][/tex]
### Step 3: Combine the Results
Now, combine the product of the coefficients and the simplified variable part.
[tex]\[ 12 \times x^5 = 12 x^5 \][/tex]
### Final Answer
The simplified form of [tex]\((3 x^2)(4 x^3)\)[/tex] is:
[tex]\[ 12 x^5 \][/tex]
Thus, among the given options, the correct answer is
[tex]\[ \boxed{12 x^5} \][/tex]
