Certainly! Let's break down the expression step-by-step:
[tex]\[
(-2)^4 + 5 \cdot \left\{[(-4) \cdot (+8) - (-7)] - \sqrt[3]{(-4)^3}\right\} - (-2)^2
\][/tex]
First, calculate each part separately:
### Step 1: Calculate [tex]\((-2)^4\)[/tex]
[tex]\[
(-2)^4 = 16
\][/tex]
### Step 2: Calculate [tex]\((-4) \cdot (+8)\)[/tex]
[tex]\[
(-4) \cdot (+8) = -32
\][/tex]
### Step 3: Simplify inside the curly braces first
[tex]\[
(-4) \cdot (+8) - (-7) = -32 + 7 = -25
\][/tex]
### Step 4: Calculate [tex]\(\sqrt[3]{(-4)^3}\)[/tex]
[tex]\[
(-4)^3 = -64
\][/tex]
The cube root of [tex]\(-64\)[/tex] is:
[tex]\[
\sqrt[3]{-64} = -3.464101615137754
\][/tex]
### Step 5: Substitute and simplify inside the curly braces
[tex]\[
-25 - (\sqrt[3]{-64}) = -25 - (-3.464101615137754) = -25 + 3.464101615137754 = -21.535898384862246
\][/tex]
### Step 6: Now, calculate the full expression in the curly braces
[tex]\[
5 \cdot (-21.535898384862246) = -107.67949192431123
\][/tex]
### Step 7: Account for [tex]\( (-2)^2 \)[/tex]
[tex]\[
(-2)^2 = 4
\][/tex]
### Step 8: Combine all parts together
[tex]\[
16 + (-107.67949192431123) - 4
\][/tex]
### Final result:
[tex]\[
16 - 107.67949192431123 - 4 = -91.67949192431123
\][/tex]
So, the final culmination of all calculations is:
[tex]\[
(-91.67949192431123)
\][/tex]
