Questions: Simplify: (2-2^2)^3/2

Simplify: (2-2^2)^3/2
Transcript text: Simplify: $\frac{\left(2-2^{2}\right)^{3}}{2}$
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Solution

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Solution Steps

To simplify the given expression, we need to follow the order of operations (PEMDAS/BODMAS). First, simplify the expression inside the parentheses, then raise it to the power of 3, and finally divide by 2.

Step 1: Simplify Inside the Parentheses

First, we simplify the expression inside the parentheses: \[ 2 - 2^2 = 2 - 4 = -2 \]

Step 2: Raise the Result to the Power of 3

Next, we raise the result from Step 1 to the power of 3: \[ (-2)^3 = -8 \]

Step 3: Divide by 2

Finally, we divide the result from Step 2 by 2: \[ \frac{-8}{2} = -4.0 \]

Final Answer

\(\boxed{-4}\)

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