In `-5p^(2)q^(3)r^(4)`, write down the coefficient of :
`p^(2)q^(2)`

Answer

To find the coefficient of \( p^2q^2 \) in the expression \( -5p^2q^3r^4 \), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ -5p^2q^3r^4 \]

### Step 2: Write down the target expression
We need to find the coefficient of:
\[ p^2q^2 \]

### Step 3: Write both expressions in expanded form
Expand both expressions:
- The expression \( -5p^2q^3r^4 \) can be written as:
\[ -5 \cdot p \cdot p \cdot q \cdot q \cdot q \cdot r \cdot r \cdot r \cdot r \]
- The expression \( p^2q^2 \) can be written as:
\[ p \cdot p \cdot q \cdot q \]

### Step 4: Divide the first expression by the second
Now, we will divide the first expression by the second:
\[ \frac{-5p^2q^3r^4}{p^2q^2} \]

### Step 5: Cancel the like terms
When we cancel the like terms:
- \( p^2 \) in the numerator cancels with \( p^2 \) in the denominator.
- \( q^2 \) in the denominator cancels with \( q^2 \) from \( q^3 \) in the numerator, leaving \( q \).

After canceling, we have:
\[ -5 \cdot q \cdot r^4 \]

### Step 6: Identify the coefficient
The remaining expression is:
\[ -5qr^4 \]
Thus, the coefficient of \( p^2q^2 \) in the original expression is:
\[ -5r^4 \]

### Final Answer
The coefficient of \( p^2q^2 \) in \( -5p^2q^3r^4 \) is:
\[ -5r^4 \]

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