Let's evaluate the given expression step-by-step:
[tex]\[
-2^2 - 5 \left[8 - \left(4 - 4^3\right)\right]
\][/tex]
### Step 1: Evaluate the inner-most expression
First, we evaluate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 64
\][/tex]
Next, substitute [tex]\(64\)[/tex] back into the expression:
[tex]\[
4 - 64 = -60
\][/tex]
### Step 2: Substitute back into the next-level expression
Substitute [tex]\(-60\)[/tex] back into the expression:
[tex]\[
8 - (-60)
\][/tex]
Calculate [tex]\(8 - (-60)\)[/tex]:
[tex]\[
8 + 60 = 68
\][/tex]
### Step 3: Substitute back into the outer expression
Now substitute [tex]\(68\)[/tex] back into the remaining expression:
[tex]\[
-2^2 - 5 \times 68
\][/tex]
### Step 4: Evaluate the base exponent and the multiplication
Evaluate the exponent:
[tex]\[
-2^2 = (-2)^2 = 4
\][/tex]
Next, multiply:
[tex]\[
5 \times 68 = 340
\][/tex]
### Step 5: Combine the results
Finally, subtract to get the result:
[tex]\[
4 - 340 = -336
\][/tex]
Therefore, the expression evaluates to:
[tex]\[
-336
\][/tex]
So, the final answer is:
[tex]\[
-336
\][/tex]
