Question

Structures of Expressions Unit Test Part 1
2 of 82 of 8 Items





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

54
54

4^2+60
4 squared plus 60

76

Answer 1

To simplify the expression \((16−12)^2 + 5(8+2^2)\) in the numerator, we can break down the steps:

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

2. Now square it:
\[
(4)^2 = 16
\]

3. Next, we need to calculate \(5(8+2^2)\):
- First, calculate \(2^2\):
\[
2^2 = 4
\]

- Then calculate \(8 + 4\):
\[
8 + 4 = 12
\]

- Now multiply by 5:
\[
5 \times 12 = 60
\]

4. Now we can combine the results:
\[
16 + 60 = 76
\]

Thus, the simplified numerator is \(76\).

The correct response is:
**76**