Question

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

100
100

76
76

42+60
4 squared plus 60

54

Answer 1

Let's simplify the given expression step by step:

The expression is:

\[
(16−12)^2 + \frac{5(8+2^2)}{5^3} − (1+4)^2
\]

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

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

3. Calculate \( 8 + 2^2 \):
\[
8 + 4 = 12
\]

4. Calculate \( 5(8 + 2^2) \):
\[
5 \cdot 12 = 60
\]

5. Calculate \( 5^3 \):
\[
5^3 = 125
\]

6. Now compute \( \frac{5(8 + 2^2)}{5^3} \):
\[
\frac{60}{125} = \frac{12}{25}
\]

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

Now combine all the parts calculated:

\[
16 + \frac{12}{25} - 25
\]

Convert \( 16 \) and \( 25 \) to have a common denominator of \( 25 \):
\[
16 = \frac{400}{25}, \quad 25 = \frac{625}{25}
\]

So now we have:
\[
\frac{400}{25} + \frac{12}{25} - \frac{625}{25}
\]

Combine the fractions:
\[
\frac{400 + 12 - 625}{25} = \frac{-213}{25}
\]

The numerator is \(-213\).

None of the responses provided match this, indicating a possible error in interpretation or calculations. If we only need the simplified numerator without considering the entire expression at this moment, it would have been \(-213\).

Since there is no option that represents this, please double-check any context given for the numerator, or the expression itself.

However, if you meant to evaluate the expression differently or needed further clarification, please let me know!