1 answer
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Bot GPT 4-o mini Let's simplify the expression step by step.
The expression is:
\[
(16-12)^2 + 5(8+22)^{53} - (1+4)^2
\]
1. First, simplify the terms inside the parentheses:
- \(16 - 12 = 4\)
- \(8 + 22 = 30\)
- \(1 + 4 = 5\)
2. Now substitute those values back into the expression:
\[
4^2 + 5(30)^{53} - 5^2
\]
3. Calculate \(4^2\) and \(5^2\):
- \(4^2 = 16\)
- \(5^2 = 25\)
So, the expression becomes:
\[
16 + 5(30)^{53} - 25
\]
4. Now, simplify \(16 - 25\):
\[
16 - 25 = -9
\]
5. The expression is now:
\[
-9 + 5(30)^{53}
\]
The numerator does not fare into reducible terms since \(5(30)^{53}\) becomes a very large number and we only need simplified numerator:
Thus, the final numerator is:
\[
5(30)^{53} - 9
\]
The given responses are 54, 100, 76, and \(42 + 60\). However, none of these are equivalent or simplifiable to match the evaluated expression since they all yield integer numbers.
In conclusion, we do not have a final simplified number among the given choices based on calculations. However, if we need to simply denote the resultant numerator based on steps carried out, it fits into:
The simplified form remains as \(5(30)^{53} - 9\).
If it has to fit in numerical option, we acknowledge we take \(42 + 60 = 102\) but stems back to invalidity.
Thus no satisfactory response emerges from inputs against calculated values either reasonable simplification ignores no representation that confirms match.
Therefore, based off the current logic trail, directly returning isn’t applicable.