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To simplify the numerator of the expression \((16−12)^2+5(8+2^2)\), we can break it down step-by-step:
1. **Calculate \(16 - 12\):**
\[
16 - 12 = 4
\]
So, \((16 - 12)^2 = 4^2 = 16\).
2. **Calculate \(2^2\):**
\[
2^2 = 4
\]
3. **Calculate \(8 + 2^2\):**
\[
8 + 2^2 = 8 + 4 = 12
\]
4. **Now calculate \(5(8 + 2^2)\):**
\[
5 \times 12 = 60
\]
5. **Add the results for the numerator:**
\[
(16) + (60) = 76
\]
Thus, the simplified numerator is \(76\). Therefore, the response is:
**76**