Consider the expression (16-12)^(2)+5 (8+2^(2)))/(5^(3)-(1+4)^(2))

Question

. What is the simplified numerator?(1 point)
Responses

100
100

4^2+60

76
76

54

Answer 1

To simplify the expression given in the numerator, we can break it down step-by-step. The numerator is:

\[ (16 - 12)^2 + 5 (8 + 2^2) \]

1. Calculate \(16 - 12\): \[ 16 - 12 = 4 \]

2. Square the result: \[ (4)^2 = 16 \]

3. Now calculate \(2^2\): \[ 2^2 = 4 \]

4. Add this to 8: \[ 8 + 4 = 12 \]

5. Multiply by 5: \[ 5 \times 12 = 60 \]

6. Now, add the two parts together: \[ 16 + 60 = 76 \]

Thus, the simplified numerator is:

\[ \boxed{76} \]