Solved on Mar 20, 2024

Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

STEP 1

Assumptions
1. We are evaluating two separate expressions.
2. The first expression is $-(7)^{2}$ .
3. The second expression is $-(-2)^{3}$ .
4. The exponent applies only to the number immediately preceding it, not the negative sign in front unless the negative sign is within parentheses.

STEP 2

Evaluate the first expression $-(7)^{2}$ . The exponent applies to the number 7, not the negative sign.
$-(7)^{2} = -(7 \times 7)$

STEP 3

Calculate the value inside the parentheses.
$-(7 \times 7) = -(49)$

STEP 4

Apply the negative sign to the result.
$-(49) = -49$

STEP 5

Evaluate the second expression $-(-2)^{3}$ . The exponent applies to the number -2, which is within the parentheses.
$-(-2)^{3} = -(-2 \times -2 \times -2)$

STEP 6

Calculate the value inside the parentheses. Remember that the product of an odd number of negative numbers is negative.
$-(-2 \times -2 \times -2) = -(-8)$

STEP 7

Apply the negative sign to the result.
$-(-8) = 8$
The evaluated expressions are:
$\begin{array}{l} -(7)^{2} = -49 \\ -(-2)^{3} = 8 \end{array}$

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Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

STEP 1

Assumptions
1. We are evaluating two separate expressions.
2. The first expression is $-(7)^{2}$ .
3. The second expression is $-(-2)^{3}$ .
4. The exponent applies only to the number immediately preceding it, not the negative sign in front unless the negative sign is within parentheses.

STEP 2

Evaluate the first expression $-(7)^{2}$ . The exponent applies to the number 7, not the negative sign.
$-(7)^{2} = -(7 \times 7)$

STEP 3

Calculate the value inside the parentheses.
$-(7 \times 7) = -(49)$

STEP 4

Apply the negative sign to the result.
$-(49) = -49$

STEP 5

Evaluate the second expression $-(-2)^{3}$ . The exponent applies to the number -2, which is within the parentheses.
$-(-2)^{3} = -(-2 \times -2 \times -2)$

STEP 6

Calculate the value inside the parentheses. Remember that the product of an odd number of negative numbers is negative.
$-(-2 \times -2 \times -2) = -(-8)$

STEP 7

Apply the negative sign to the result.
$-(-8) = 8$
The evaluated expressions are:
$\begin{array}{l} -(7)^{2} = -49 \\ -(-2)^{3} = 8 \end{array}$

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Evaluate the expressions: −(7)2-(7)^{2}−(7)2 and −(−2)3-(-2)^{3}−(−2)3.

STEP 1

STEP 2

Evaluate the first expression −(7)2-(7)^{2}−(7)2. The exponent applies to the number 7, not the negative sign.−(7)2=−(7×7)-(7)^{2} = -(7 \times 7)−(7)2=−(7×7)

STEP 3

Calculate the value inside the parentheses.−(7×7)=−(49)-(7 \times 7) = -(49)−(7×7)=−(49)

STEP 4

Apply the negative sign to the result.−(49)=−49-(49) = -49−(49)=−49

STEP 5

Evaluate the second expression −(−2)3-(-2)^{3}−(−2)3. The exponent applies to the number -2, which is within the parentheses.−(−2)3=−(−2×−2×−2)-(-2)^{3} = -(-2 \times -2 \times -2)−(−2)3=−(−2×−2×−2)

STEP 6

Calculate the value inside the parentheses. Remember that the product of an odd number of negative numbers is negative.−(−2×−2×−2)=−(−8)-(-2 \times -2 \times -2) = -(-8)−(−2×−2×−2)=−(−8)

STEP 7

Apply the negative sign to the result.−(−8)=8-(-8) = 8−(−8)=8The evaluated expressions are:−(7)2=−49−(−2)3=8 \begin{array}{l} -(7)^{2} = -49 \\ -(-2)^{3} = 8 \end{array} −(7)2=−49−(−2)3=8​

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Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

Evaluate the first expression $-(7)^{2}$ . The exponent applies to the number 7, not the negative sign.
$-(7)^{2} = -(7 \times 7)$

Calculate the value inside the parentheses.
$-(7 \times 7) = -(49)$

Apply the negative sign to the result.
$-(49) = -49$

Evaluate the second expression $-(-2)^{3}$ . The exponent applies to the number -2, which is within the parentheses.
$-(-2)^{3} = -(-2 \times -2 \times -2)$

Calculate the value inside the parentheses. Remember that the product of an odd number of negative numbers is negative.
$-(-2 \times -2 \times -2) = -(-8)$

Apply the negative sign to the result.
$-(-8) = 8$
The evaluated expressions are:
$\begin{array}{l} -(7)^{2} = -49 \\ -(-2)^{3} = 8 \end{array}$