Questions: or to compute each of the following. e) -8^3 - ∛(-8) =

Transcript text: or to compute each of the following. e) $-8^{3}-\sqrt[3]{-8}=$

Solution

Step 1: Calculate $ -8^3 $

We first calculate the cube of $-8$: \[ -8^3 = -512 \]

Step 2: Calculate $ \sqrt[3]{-8} $

Next, we find the cube root of $-8$: \[ \sqrt[3]{-8} = 1 + \sqrt{3}i \] This result is a complex number, specifically $ (1.0000 + 1.7321i) $.

Step 3: Combine the Results

Now, we subtract the cube root from the cube: \[ -512 - (1 + \sqrt{3}i) = -513 - \sqrt{3}i \]

The final result of the expression $ -8^3 - \sqrt[3]{-8} $ is: \[ \boxed{-513 - \sqrt{3}i} \]

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