In `(5)/(7)xy^(2)z^(3)`, write the coefficient of :
`z^(3)`

Answer

To find the coefficient of \( z^3 \) in the expression \( \frac{5}{7} xy^2 z^3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the expression**: We start with the expression \( \frac{5}{7} xy^2 z^3 \).

2. **Understand the term 'coefficient'**: The coefficient of a term in an algebraic expression is the numerical factor that multiplies the variable(s). In this case, we need to find the coefficient of \( z^3 \).

3. **Factor out \( z^3 \)**: We can rewrite the expression by factoring out \( z^3 \):
\[ \frac{5}{7} xy^2 z^3 = z^3 \left( \frac{5}{7} xy^2 \right) \]
Here, we have taken \( z^3 \) out, and what remains is \( \frac{5}{7} xy^2 \).

4. **Identify the coefficient**: The expression inside the parentheses, \( \frac{5}{7} xy^2 \), is the coefficient of \( z^3 \).

5. **Conclusion**: Therefore, the coefficient of \( z^3 \) in the expression \( \frac{5}{7} xy^2 z^3 \) is:
\[ \frac{5}{7} xy^2 \]

### Final Answer:
The coefficient of \( z^3 \) is \( \frac{5}{7} xy^2 \).

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