In `-7xy^(2)z^(3)`. write down the coefficient of:
`7yz^(2)`

Answer

To find the coefficient of \( 7yz^{2} \) in the expression \( -7xy^{2}z^{3} \), we can follow these steps:

### Step 1: Identify the expression
We start with the expression \( -7xy^{2}z^{3} \).

### Step 2: Break down the expression
We can express \( -7xy^{2}z^{3} \) in product form:
\[ -7xy^{2}z^{3} = -7 \cdot x \cdot y \cdot y \cdot z \cdot z \cdot z \]

### Step 3: Identify the target term
We need to find the coefficient of the term \( 7yz^{2} \).

### Step 4: Compare terms
The term \( 7yz^{2} \) can be broken down into:
\[ 7 \cdot y \cdot z \cdot z \]
This means we have \( 7 \) as the constant, \( y \) as the variable, and \( z^{2} \) as \( z \cdot z \).

### Step 5: Determine the remaining factors
To find the coefficient, we need to look at what remains from the original expression after accounting for \( 7yz^{2} \):
- From \( -7xy^{2}z^{3} \), we have already used \( 7 \), \( y \), and \( z \cdot z \).
- The remaining factors are \( -x \) and \( z \) (since we used two \( z \)s from \( z^{3} \)).

### Step 6: Write the coefficient
Thus, the coefficient of \( 7yz^{2} \) in \( -7xy^{2}z^{3} \) is:
\[ -xz \]

### Final Answer
The coefficient of \( 7yz^{2} \) in \( -7xy^{2}z^{3} \) is \( -xz \).

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