Find the product of :
`-5a^(2)b and 4b^(2) c`

Answer

To find the product of the expressions \(-5a^{2}b\) and \(4b^{2}c\), we will follow these steps:

### Step 1: Write down the expressions
We have the two expressions:
\[ -5a^{2}b \quad \text{and} \quad 4b^{2}c \]

### Step 2: Multiply the coefficients
First, we multiply the numerical coefficients:
\[ -5 \times 4 = -20 \]

### Step 3: Multiply the variable \(a\)
The variable \(a\) appears only in the first expression:
\[ a^{2} \quad \text{(there is no \(a\) in the second expression)} \]

### Step 4: Multiply the variable \(b\)
Now, we multiply the \(b\) terms:
\[ b \times b^{2} = b^{1+2} = b^{3} \]

### Step 5: Include the variable \(c\)
The variable \(c\) appears only in the second expression:
\[ c \quad \text{(there is no \(c\) in the first expression)} \]

### Step 6: Combine all parts
Now, we combine all the parts we calculated:
\[ -20a^{2}b^{3}c \]

### Final Answer
Thus, the product of \(-5a^{2}b\) and \(4b^{2}c\) is:
\[ \boxed{-20a^{2}b^{3}c} \]

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