Let's simplify the expression step by step:
\[ (16 - 12)^2 + 5(8 + 2^2) / 5^3 - (1 + 4)^2 \]
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Calculate \( (16 - 12)^2 \): \[ (4)^2 = 16 \]
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Calculate \( 2^2 \): \[ 2^2 = 4 \]
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Substitute back into the expression and simplify \( 5(8 + 2^2) \): \[ 8 + 4 = 12 \quad \Rightarrow \quad 5(12) = 60 \]
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Calculate \( 5^3 \): \[ 5^3 = 125 \]
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Now evaluate \( \frac{60}{125} \): \[ \frac{60}{125} = \frac{12}{25} \]
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Next, calculate \( (1 + 4)^2 \): \[ (5)^2 = 25 \]
Putting all this together: \[ 16 + \frac{12}{25} - 25 \]
Convert \( 16 \) into a fraction with a denominator of 25: \[ 16 = \frac{400}{25} \quad \Rightarrow \quad \frac{400}{25} + \frac{12}{25} - \frac{625}{25} \]
Now combine the fractions: \[ \frac{400 + 12 - 625}{25} = \frac{412 - 625}{25} = \frac{-213}{25} \]
The numerator of the simplified expression is \(-213\).
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