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

Answer

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

### Step-by-Step Solution:

1. **Identify the Expression**:
The given expression is \( \frac{5}{7}xy^2z^3 \).

2. **Recognize the Coefficient**:
The coefficient of a term in an algebraic expression is the numerical factor that multiplies the variable part. In this case, we are looking for the coefficient of the term \( 5xy^2 \).

3. **Rearranging the Expression**:
We can rewrite the expression to clearly see the term \( 5xy^2 \):
\[ \frac{5}{7}xy^2z^3 = \left(\frac{5}{7}z^3\right)(xy^2) \]
Here, \( xy^2 \) is the term we are interested in, and \( \frac{5}{7}z^3 \) is the coefficient of that term.

4. **Extract the Coefficient**:
From the rearranged expression, we can see that the coefficient of \( 5xy^2 \) is \( \frac{5}{7}z^3 \).

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