Divide :
`-14x^(6)y^(3) - 21x^(4)y^(5) + 7x^(5)y^(4)` by `7x^(2)y^(2)`

Answer

To solve the problem of dividing the expression \(-14x^6y^3 - 21x^4y^5 + 7x^5y^4\) by \(7x^2y^2\), we can follow these steps:

### Step 1: Write the expression to be divided
We start with the expression:
\[ -14x^6y^3 - 21x^4y^5 + 7x^5y^4 \]
and we want to divide it by:
\[ 7x^2y^2 \]

### Step 2: Divide each term separately
We will divide each term of the polynomial by \(7x^2y^2\).

1. **First term:**
\[ \frac{-14x^6y^3}{7x^2y^2} \]
- Divide the coefficients: \(-14 \div 7 = -2\)
- For \(x\): \(x^6 \div x^2 = x^{6-2} = x^4\)
- For \(y\): \(y^3 \div y^2 = y^{3-2} = y^1\)
- Result: \(-2x^4y\)

2. **Second term:**
\[ \frac{-21x^4y^5}{7x^2y^2} \]
- Divide the coefficients: \(-21 \div 7 = -3\)
- For \(x\): \(x^4 \div x^2 = x^{4-2} = x^2\)
- For \(y\): \(y^5 \div y^2 = y^{5-2} = y^3\)
- Result: \(-3x^2y^3\)

3. **Third term:**
\[ \frac{7x^5y^4}{7x^2y^2} \]
- Divide the coefficients: \(7 \div 7 = 1\)
- For \(x\): \(x^5 \div x^2 = x^{5-2} = x^3\)
- For \(y\): \(y^4 \div y^2 = y^{4-2} = y^2\)
- Result: \(x^3y^2\)

### Step 3: Combine the results
Now we can combine the results from each term:
\[ -2x^4y - 3x^2y^3 + x^3y^2 \]

### Final Answer
The final result of the division is:
\[ -2x^4y - 3x^2y^3 + x^3y^2 \]