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

Answer

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

### Step 1: Identify the expression
The given expression is:
\[ -7xy^2z^3 \]

### Step 2: Write the expression in product form
We can express the given expression in product form:
\[ -7 \cdot x \cdot y \cdot y \cdot z \cdot z \cdot z \]
This shows that \( y \) appears twice and \( z \) appears three times.

### Step 3: Identify the coefficient of \( xyz \)
To find the coefficient of \( xyz \), we need to consider how many times \( x \), \( y \), and \( z \) appear in the expression.

In \( -7xy^2z^3 \):
- The coefficient of \( x \) is \( -7 \).
- The coefficient of \( y \) is \( y^2 \) (which means \( y \) appears twice).
- The coefficient of \( z \) is \( z^3 \) (which means \( z \) appears three times).

### Step 4: Write the remaining terms
To find the coefficient of \( xyz \), we need to consider the remaining terms after taking one \( x \), one \( y \), and one \( z \):
\[ \text{Remaining terms} = -7 \cdot y \cdot z^2 \]
This simplifies to:
\[ -7yz^2 \]

### Step 5: Conclusion
Thus, the coefficient of \( xyz \) in the expression \( -7xy^2z^3 \) is:
\[ -7y z^2 \]

### Final Answer
The coefficient of \( xyz \) is \( -7y z^2 \).

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