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

Answer

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

1. **Identify the Given Expression**: The expression we are working with is \( \frac{5}{7} xy^2 z^3 \).

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

3. **Factor Out \( xy^2 \)**: To find the coefficient of \( xy^2 \), we can factor \( xy^2 \) out of the expression. The expression can be rewritten as:
\[ \frac{5}{7} xy^2 z^3 = xy^2 \left( \frac{5}{7} z^3 \right) \]

4. **Identify the Coefficient**: From the factored expression, we can see that the coefficient of \( xy^2 \) is the remaining part after factoring out \( xy^2 \), which is:
\[ \frac{5}{7} z^3 \]

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

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

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