Find the value of the expressions, when `a= -1" and "b= 3`
`5a^(2)+4ab^(2)-8a^(2)b`.

Answer

To find the value of the expression \( 5a^2 + 4ab^2 - 8a^2b \) when \( a = -1 \) and \( b = 3 \), we will substitute the values of \( a \) and \( b \) into the expression step by step.

### Step 1: Substitute the values of \( a \) and \( b \)
We start with the expression:
\[ 5a^2 + 4ab^2 - 8a^2b \]
Substituting \( a = -1 \) and \( b = 3 \):
\[ 5(-1)^2 + 4(-1)(3)^2 - 8(-1)^2(3) \]

### Step 2: Calculate \( a^2 \) and \( b^2 \)
Calculate \( (-1)^2 \) and \( (3)^2 \):
\[ (-1)^2 = 1 \quad \text{and} \quad (3)^2 = 9 \]
Now substitute these values back into the expression:
\[ 5(1) + 4(-1)(9) - 8(1)(3) \]

### Step 3: Simplify each term
Now simplify each term:
1. \( 5(1) = 5 \)
2. \( 4(-1)(9) = -36 \)
3. \( -8(1)(3) = -24 \)

Now the expression looks like:
\[ 5 - 36 - 24 \]

### Step 4: Combine the terms
Now combine the terms:
\[ 5 - 36 = -31 \]
Then,
\[ -31 - 24 = -55 \]

### Final Answer
Thus, the value of the expression \( 5a^2 + 4ab^2 - 8a^2b \) when \( a = -1 \) and \( b = 3 \) is:
\[ \boxed{-55} \]