Multiply :
`8ab^(2)` by `-4a^(3)b^(4)`

Answer

To multiply the algebraic expressions \(8ab^2\) and \(-4a^3b^4\), we will follow these steps:

### Step 1: Multiply the coefficients
First, we multiply the numerical coefficients of the two expressions:
\[ 8 \times (-4) = -32 \]

### Step 2: Multiply the variables with the same base
Next, we multiply the variables. We will use the property of exponents that states when multiplying like bases, we add the exponents.

- For \(a\):
\[ a^1 \times a^3 = a^{1+3} = a^4 \]

- For \(b\):
\[ b^2 \times b^4 = b^{2+4} = b^6 \]

### Step 3: Combine the results
Now we combine the results from Steps 1 and 2:
\[ -32a^4b^6 \]

### Final Answer
Thus, the product of \(8ab^2\) and \(-4a^3b^4\) is:
\[ \boxed{-32a^4b^6} \]

---