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

Answer

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

### Step 1: Identify the given expression
The given expression is:
\[ \frac{5}{7}xy^2z^3 \]

### Step 2: Write \( yz^2 \) in terms of the variables
We need to express \( yz^2 \) in terms of the variables present in the expression. We can see that:
\[ yz^2 = y \cdot z \cdot z \]

### Step 3: Break down the expression
Now, we can break down the expression \( \frac{5}{7}xy^2z^3 \) into its individual components:
\[ \frac{5}{7} \cdot x \cdot y \cdot y \cdot z \cdot z \cdot z \]
This shows that we have:
- 2 \( y \) terms
- 3 \( z \) terms

### Step 4: Identify the terms needed for \( yz^2 \)
To find \( yz^2 \), we need:
- 1 \( y \) from \( y^2 \) (which leaves us with 1 \( y \))
- 2 \( z \) from \( z^3 \) (which leaves us with 1 \( z \))

### Step 5: Write the remaining terms
After taking \( yz^2 \) from the original expression, the remaining terms are:
\[ \frac{5}{7} \cdot x \cdot y \cdot z \]

### Step 6: Identify the coefficient
The coefficient of \( yz^2 \) is therefore:
\[ \frac{5}{7}xy \]

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

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