Questions: =[((2/3)((2)-3)^(3 / 2))-(2(2)-(2)^2)]-[0]

Transcript text: $=\left[\left(\frac{2}{3}((2)-3)^{3 / 2}\right)-\left(2(2)-(2)^{2}\right)\right]-[0]$

Solution

Solution Steps

Step 1: Evaluate the Inner Expression

We start by evaluating the inner expression: \[ 2 - 3 = -1 \]

Step 2: Raise to the Power of $ \frac{3}{2} $

Next, we raise the result from Step 1 to the power of $ \frac{3}{2} $: \[ (-1)^{\frac{3}{2}} = -1 \cdot i = -1 + 0i \] This results in a complex number: \[ (-1.8369701987210297 \times 10^{-16} - 1j) \]

Step 3: Multiply by $ \frac{2}{3} $

We then multiply the result from Step 2 by $ \frac{2}{3} $: \[ \frac{2}{3} \cdot (-1 + 0i) = -\frac{2}{3} + 0i \] This gives us: \[ (-1.224646799147353 \times 10^{-16} - 0.6666666666666666j) \]

Step 4: Evaluate the Expression $ 2(2) - (2)^2 $

Now we evaluate the expression $ 2(2) - (2)^2 $: \[ 2 \cdot 2 - 2^2 = 4 - 4 = 0 \]

Step 5: Subtract the Result from Step 4 from Step 3

We subtract the result from Step 4 from the result of Step 3: \[ (-1.224646799147353 \times 10^{-16} - 0.6666666666666666j) - 0 = (-1.224646799147353 \times 10^{-16} - 0.6666666666666666j) \]