To find the product of [tex]\(\left(3 a^2 b^4\right)\left(-8 a b^3\right)\)[/tex], we need to multiply the coefficients and add the exponents of like variables.
### Step-by-Step Solution
Step 1: Multiply the coefficients
First, let's multiply the numerical coefficients:
[tex]\[
3 \times (-8) = -24
\][/tex]
Step 2: Add the exponents of [tex]\(a\)[/tex]
Next, we will add the exponents of [tex]\(a\)[/tex]:
[tex]\[
2 + 1 = 3
\][/tex]
Step 3: Add the exponents of [tex]\(b\)[/tex]
Now, we add the exponents of [tex]\(b\)[/tex]:
[tex]\[
4 + 3 = 7
\][/tex]
Step 4: Combine the results
Putting it all together, the product is:
[tex]\[
-24a^3b^7
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-24a^3b^7}
\][/tex]
