To simplify the expression \(3 + (7 - 4^3)\), let's break it down step by step.
Calculate \(4^3\): \[ 4^3 = 4 \times 4 \times 4 = 64 \]
Substitute \(4^3\) back into the expression: \[ 3 + (7 - 64) \]
Now calculate \(7 - 64\): \[ 7 - 64 = -57 \]
Substitute \(-57\) back into the expression: \[ 3 + (-57) = 3 - 57 \]
Finally, calculate \(3 - 57\): \[ 3 - 57 = -54 \]
Thus, the simplified value of the expression \(3 + (7 - 4^3)\) is \(-54\).