Let's find the product of the given expressions:
[tex]\[
\left(3 a^2 b^4\right)\left(-8 a b^3\right)
\][/tex]
We will break this down into steps:
1. Product of the coefficients:
[tex]\[
3 \times (-8) = -24
\][/tex]
2. Product of the [tex]\(a\)[/tex] terms:
[tex]\[
a^2 \times a^1 = a^{2+1} = a^3
\][/tex]
3. Product of the [tex]\(b\)[/tex] terms:
[tex]\[
b^4 \times b^3 = b^{4+3} = b^7
\][/tex]
Combining the results from these three steps, we get:
[tex]\[
-24 a^3 b^7
\][/tex]
Thus, the product of [tex]\(\left(3 a^2 b^4\right)\left(-8 a b^3\right)\)[/tex] is:
[tex]\[
\boxed{-24 a^3 b^7}
\][/tex]
