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

Options

A. `(5)/(7)`
B. `(5)/(7)xy^(2)z^(3)`
C. `(5)/(7)xy^(2)`
D. `(5)/(7)xy^(2)z^(2)`

Answer

To find the coefficient of \( z \) 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. **Understand what a coefficient is**:
The coefficient of a variable in an algebraic expression is the numerical factor that multiplies that variable. In this case, we need to find the coefficient of \( z \).

3. **Separate the terms**:
We can rewrite the expression to clearly see the coefficient of \( z \):
\[ \frac{5}{7} \cdot x \cdot y^2 \cdot z^3 \]

4. **Identify the coefficient of \( z \)**:
In the term \( z^3 \), the coefficient is the product of all the numerical factors that are not part of \( z \). Here, the coefficient of \( z^3 \) is \( \frac{5}{7}xy^2 \).

5. **Write the coefficient of \( z \)**:
Since we are looking for the coefficient of \( z \) specifically, we note that \( z^3 \) can be expressed as \( z \cdot z \cdot z \). Thus, the coefficient of \( z \) in \( z^3 \) is the same as the coefficient of \( z^1 \), which is \( \frac{5}{7}xy^2z^2 \).

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