Certainly! Let's find the product of the given terms step-by-step.
We need to multiply the two algebraic expressions:
[tex]\[ \left(3 a^2 b^4\right)\left(-8 a b^3\right) \][/tex]
### 1. Multiply the coefficients:
The coefficients are:
[tex]\[ 3 \quad \text{and} \quad -8 \][/tex]
Multiplying these together, we get:
[tex]\[ 3 \times -8 = -24 \][/tex]
### 2. Calculate the exponents for [tex]\( a \)[/tex]:
The exponents of [tex]\( a \)[/tex] in the two terms are:
[tex]\[ 2 \quad \text{and} \quad 1 \][/tex]
Adding these together, we get:
[tex]\[ 2 + 1 = 3 \][/tex]
So, the exponent of [tex]\( a \)[/tex] in the product is [tex]\( 3 \)[/tex].
### 3. Calculate the exponents for [tex]\( b \)[/tex]:
The exponents of [tex]\( b \)[/tex] in the two terms are:
[tex]\[ 4 \quad \text{and} \quad 3 \][/tex]
Adding these together, we get:
[tex]\[ 4 + 3 = 7 \][/tex]
So, the exponent of [tex]\( b \)[/tex] in the product is [tex]\( 7 \)[/tex].
### 4. Combine everything into the final product:
Now we combine our results:
[tex]\[ -24 a^3 b^7 \][/tex]
Thus, the product is:
[tex]\[ \boxed{-24 a^3 b^7} \][/tex]
