To solve the expression \(|24 + 2^3| \times (2 + 8)^2\), let's break it down step by step.
Calculate \(2^3\): \[ 2^3 = 8 \]
Add 24 to \(2^3\): \[ 24 + 8 = 32 \]
Take the absolute value: \[ |32| = 32 \]
Now calculate \(2 + 8\): \[ 2 + 8 = 10 \]
Square the result: \[ (10)^2 = 100 \]
Now multiply the absolute value by the squared result: \[ 32 \times 100 = 3200 \]
Thus, the final result is: \[ \boxed{3200} \]