The product of `(3m^2n^7(-4m^4n^3)` is equivalent to :

Options

A. `-12 m^5 n^10`
B. `-12m^4 n^4`
C. `-12m^12n^4`
D. `-12m^6n^10`

Answer

To find the product of \( (3m^2n^7) \) and \( (-4m^4n^3) \), we will follow these steps:

### Step 1: Multiply the coefficients
We start by multiplying the numerical coefficients of the two terms:
\[ 3 \times (-4) = -12 \]

### Step 2: Multiply the \( m \) terms
Next, we multiply the \( m \) terms. We use the property of exponents that states \( a^b \times a^c = a^{b+c} \):
\[ m^2 \times m^4 = m^{2+4} = m^6 \]

### Step 3: Multiply the \( n \) terms
Now, we multiply the \( n \) terms using the same property of exponents:
\[ n^7 \times n^3 = n^{7+3} = n^{10} \]

### Step 4: Combine all parts
Now we combine all the parts we calculated:
\[ -12 \times m^6 \times n^{10} = -12m^6n^{10} \]

### Final Answer
Thus, the product of \( (3m^2n^7) \) and \( (-4m^4n^3) \) is:
\[ \boxed{-12m^6n^{10}} \]

---