Question
Use the order of operations to simplify the given expression. \[ -2 \cdot\left[16 \div(8-4)^{2}\right]^{2} \]
Ask by George Griffiths. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(-2\).
Solution
1. Begin with the original expression:
\[
-2 \cdot\left[16 \div(8-4)^{2}\right]^{2}
\]
2. Evaluate the expression inside the parentheses \((8-4)\):
\[
8-4 = 4
\]
3. Square the result:
\[
(8-4)^{2} = 4^{2} = 16
\]
4. Perform the division:
\[
16 \div 16 = 1
\]
5. Square the result of the division:
\[
\left[1\right]^{2} = 1
\]
6. Multiply by \(-2\):
\[
-2 \cdot 1 = -2
\]
The simplified expression is:
\[
-2
\]
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Simplify this solution The Deep Dive
To simplify the expression \(-2 \cdot\left[16 \div(8-4)^{2}\right]^{2}\), we follow the order of operations: 1. **Parentheses**: Start with the operation inside the parentheses: \[ 8 - 4 = 4 \] 2. **Exponent**: Next, compute the exponent: \[ (4)^{2} = 16 \] 3. **Division**: Now, substitute back into the expression and perform the division: \[ 16 \div 16 = 1 \] 4. **Square**: Now we square the result: \[ 1^{2} = 1 \] 5. **Multiplication**: Finally, multiply by \(-2\): \[ -2 \cdot 1 = -2 \] Thus, the simplified expression is \(-2\).
