Consider the expression (16−12)^2+5(8+2^2)5^3−(1+4)^2 . What is the simplified numerator?(1 point)

Question

Responses

76
76

100
100

54
54

4^2+60

Answer 1

Let's simplify the expression step by step:

The expression is given as:

\[ (16 - 12)^2 + 5(8 + 2^2) \cdot 5^3 - (1 + 4)^2 \]

1. Calculate \( (16 - 12)^2 \): \[ 16 - 12 = 4 \implies (4)^2 = 16 \]

2. Calculate \( (1 + 4)^2 \): \[ 1 + 4 = 5 \implies (5)^2 = 25 \]

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

4. Now calculate \( 8 + 2^2 \): \[ 8 + 4 = 12 \]

5. Then calculate \( 5(12) \): \[ 5 \cdot 12 = 60 \]

6. Now calculate \( 5^3 \): \[ 5^3 = 125 \]

7. Now calculate \( 5(12) \cdot 5^3 \): \[ 60 \cdot 125 = 7500 \]

8. Now substitute everything back into the expression: \[ 16 + 7500 - 25 \]

9. Calculate \( 16 - 25 \): \[ 16 - 25 = -9 \]

10. Now, add \( 7500 \): \[ -9 + 7500 = 7491 \]

So, the simplified numerator of the expression is \( 7491 \).

Given the provided options, it looks like there is no matching answer in the choices:

• \( 76 \)
• \( 100 \)
• \( 54 \)
• \( 4^2 + 60 \)

Thus, none of the choices are correct based on the simplification performed.