Pregunta
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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Expression 17 is negative, and Expression 18 is positive.
Solución
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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