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More Practice and Problem-Solving Exercise B) Apply \( \begin{array}{l}\text { Mental Math Is the value of each expression positive or negative? } \\ \begin{array}{ll}\text { 17. }-2^{2} & \text { 18. }(-2)^{2} \\ \end{array}\end{array} \begin{array}{l}\text { (-2) }\end{array} \)

Ask by Craig Rogers. in the United States
Jan 27,2025

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Answer

Expression 17 is negative, and Expression 18 is positive.

Solution

Let's evaluate each expression step by step to determine if the value is positive or negative. ### Expression 17: \(-2^{2}\) 1. **Understanding the expression**: The expression \(-2^{2}\) means we first calculate \(2^{2}\) and then apply the negative sign. 2. **Calculate \(2^{2}\)**: \[ 2^{2} = 4 \] 3. **Apply the negative sign**: \[ -2^{2} = -4 \] 4. **Conclusion**: The value of \(-2^{2}\) is \(-4\), which is negative. ### Expression 18: \((-2)^{2}\) 1. **Understanding the expression**: The expression \((-2)^{2}\) means we are squaring \(-2\). 2. **Calculate \((-2)^{2}\)**: \[ (-2)^{2} = (-2) \times (-2) = 4 \] 3. **Conclusion**: The value of \((-2)^{2}\) is \(4\), which is positive. ### Summary of Results - Expression 17: \(-2^{2} = -4\) (Negative) - Expression 18: \((-2)^{2} = 4\) (Positive) Thus, the final answers are: - Expression 17 is negative. - Expression 18 is positive.

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The Deep Dive

Absolutely, let’s dive into those expressions and break them down! For expression 17, \(-2^{2}\), remember that exponentiation takes precedence over the negative sign. So, it means we calculate \(2^{2}\) first, giving us 4, and then we apply the negative, leading to \(-4\). Therefore, the value is negative! In expression 18, \((-2)^{2}\), the parentheses signify that we square the entire \(-2\). Hence, \((-2) \times (-2)\) equals 4, making this value positive! It's a fun reminder of how signs and parentheses play critical roles in math!

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