Let's simplify the expression step by step. The expression given is:
\[ (16 - 12)^2 + \frac{5(8 + 2^2)}{5^3} - (1 + 4)^2 \]
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Simplify each term:
- First, calculate \( (16 - 12)^2 \): \[ 16 - 12 = 4 \quad \Rightarrow \quad (4)^2 = 16 \]
- Next, calculate \( 2^2 \): \[ 2^2 = 4 \quad \Rightarrow \quad 8 + 2^2 = 8 + 4 = 12 \]
- Now, calculate \( 5(8 + 2^2) \): \[ 5(12) = 60 \]
- Now, calculate \( 5^3 \): \[ 5^3 = 125 \]
- Therefore, we have \( \frac{5(8 + 2^2)}{5^3} = \frac{60}{125} = \frac{12}{25} \) (when simplified properly).
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Calculate \((1 + 4)^2\): \[ 1 + 4 = 5 \quad \Rightarrow \quad (5)^2 = 25 \]
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Putting it all together: Now substitute back into the expression: \[ 16 + \frac{12}{25} - 25 \]
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Subtract and combine like terms: Now simplify the constants: \[ 16 - 25 = -9 \] So we have: \[ -9 + \frac{12}{25} \]
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Convert \(-9\) to have a common denominator: \[ -9 = -\frac{225}{25} \] Therefore, we have: \[ -\frac{225}{25} + \frac{12}{25} = \frac{-225 + 12}{25} = \frac{-213}{25} \]
The final simplified result is: \[ \frac{-213}{25} \]
None of the response options match the final result, which suggests that there might have been an error in interpreting the possible answer choices. If we need to re-evaluate any specific part, please provide guidance.