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

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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)
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