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

Answer

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

### Step 1: Identify the expressions
We have two expressions:
1. The main expression: \(-5p^2q^3r^4\)
2. The expression we are interested in: \(-pq^2r^3\)

### Step 2: Write the main expression in expanded form
The main expression can be written as:
\[ -5p^2q^3r^4 = -5 \cdot p^2 \cdot q^3 \cdot r^4 \]

### Step 3: Write the second expression in expanded form
The second expression can be written as:
\[ -pq^2r^3 = -1 \cdot p^1 \cdot q^2 \cdot r^3 \]

### Step 4: Divide the main expression by the second expression
To find the coefficient, we can divide the main expression by the second expression:
\[ \frac{-5p^2q^3r^4}{-pq^2r^3} \]

### Step 5: Simplify the division
When we divide, we can cancel out the like terms:
- The negative signs cancel out.
- \(p^2\) divided by \(p^1\) gives \(p^{2-1} = p^1\).
- \(q^3\) divided by \(q^2\) gives \(q^{3-2} = q^1\).
- \(r^4\) divided by \(r^3\) gives \(r^{4-3} = r^1\).

So, we have:
\[ \frac{-5p^2q^3r^4}{-pq^2r^3} = 5pq^1r^1 \]

### Step 6: Identify the coefficient
The coefficient of the expression \(-pq^2r^3\) in \(-5p^2q^3r^4\) is \(5qr\).

### Final Answer
Thus, the coefficient of \(-pq^2r^3\) in \(-5p^2q^3r^4\) is:
\[ 5qr \]

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