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

Answer

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

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

### Step 2: Write down the term we are interested in
We need to find the coefficient of the term:
\[ 5xyz \]

### Step 3: Break down the expression
We can rewrite the expression by separating the variables:
\[ \frac{5}{7} \cdot x \cdot y^2 \cdot z^3 = \frac{5}{7} \cdot x \cdot (y \cdot y) \cdot (z \cdot z \cdot z) \]

### Step 4: Identify the components of \( 5xyz \)
The term \( 5xyz \) consists of:
- The coefficient \( 5 \)
- The variable \( x \)
- The variable \( y \)
- The variable \( z \)

### Step 5: Separate the remaining terms
To find the coefficient of \( 5xyz \), we can take \( 5xyz \) from the expression and see what remains:
- From \( \frac{5}{7}xy^2z^3 \), we can take \( 5xyz \) out, leaving:
\[ \frac{5}{7} \cdot x \cdot y \cdot y \cdot z \cdot z \cdot z = 5xyz \cdot \left(\frac{1}{7} \cdot y \cdot z^2\right) \]

### Step 6: Write the coefficient
The coefficient of \( 5xyz \) is what remains in front of \( 5xyz \):
\[ \frac{1}{7} \cdot y \cdot z^2 \]

### Step 7: Finalize the coefficient
Thus, the coefficient of \( 5xyz \) in the expression \( \frac{5}{7}xy^2z^3 \) is:
\[ \frac{1}{7}y z^2 \]

### Summary
The coefficient of \( 5xyz \) in the expression \( \frac{5}{7}xy^2z^3 \) is \( \frac{1}{7}y z^2 \).

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