Write the numerical coefficient of each term of the expression :
`x^(4)-5xy^(2)+7x^(2)-(2)/(3)x-(1)/(2)`.

Answer

To find the numerical coefficient of each term in the expression \( x^4 - 5xy^2 + 7x^2 - \frac{2}{3}x - \frac{1}{2} \), we will analyze each term step by step.

### Step-by-Step Solution:

1. **Identify the first term:**
- The first term is \( x^4 \).
- The numerical coefficient is the constant factor in front of the variable. Since \( x^4 \) can be written as \( 1 \cdot x^4 \), the numerical coefficient is **1**.

2. **Identify the second term:**
- The second term is \( -5xy^2 \).
- The numerical coefficient here is the constant factor, which is **-5**.

3. **Identify the third term:**
- The third term is \( 7x^2 \).
- The numerical coefficient is the constant factor, which is **7**.

4. **Identify the fourth term:**
- The fourth term is \( -\frac{2}{3}x \).
- The numerical coefficient is the constant factor, which is **-\frac{2}{3}**.

5. **Identify the fifth term:**
- The fifth term is \( -\frac{1}{2} \).
- This term does not have a variable associated with it, so it does not have a numerical coefficient in the context of variables. However, if we consider it as a standalone constant, we can say the coefficient is **-1/2** (though it's not associated with a variable).

### Summary of Numerical Coefficients:
- For \( x^4 \): **1**
- For \( -5xy^2 \): **-5**
- For \( 7x^2 \): **7**
- For \( -\frac{2}{3}x \): **-\frac{2}{3}**
- For \( -\frac{1}{2} \): **-1/2** (as a constant)