Question

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