The product of `(-4x^6 y^7)(-2xy^3)` is :

Options

A. `8x^7y^10`
B. `8x^6y^10`
C. `8x^6y^21`
D. `8x^7y^21`

Answer

To find the product of the expressions \((-4x^6 y^7)\) and \((-2xy^3)\), we will follow these steps:

### Step 1: Multiply the coefficients
We start by multiplying the numerical coefficients of the two expressions:
\[ -4 \times -2 = 8 \]

### Step 2: Multiply the \(x\) terms
Next, we multiply the \(x\) terms. We have:
\[ x^6 \times x^1 = x^{6+1} = x^7 \]

### Step 3: Multiply the \(y\) terms
Now, we multiply the \(y\) terms:
\[ y^7 \times y^3 = y^{7+3} = y^{10} \]

### Step 4: Combine all parts
Now we combine all the results from the previous steps:
\[ 8x^7y^{10} \]

### Final Answer
Thus, the product of \((-4x^6 y^7)(-2xy^3)\) is:
\[ \boxed{8x^7y^{10}} \]

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