Question

Simplify the expression below using order of operations.
open square bracket, left parenthesis, minus, 4, plus, 2, right parenthesis, minus, left parenthesis, 7, to the power 1 , plus, 5, right parenthesis, close square bracket, minus, left parenthesis, minus, 5, right parenthesis, minus, 5
[(−4+2)−(7
1
+5)]−(−5)−5

Answer 1

To simplify the expression \([(−4 + 2) − (7^1 + 5)] − (−5) − 5\), we'll use the order of operations (parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right)).

1. Start with the expression:
\[
[(−4 + 2) − (7^1 + 5)] − (−5) − 5
\]

2. Calculate \(−4 + 2\):
\[
−4 + 2 = −2
\]

3. Calculate \(7^1 + 5\):
\[
7^1 = 7 \quad \text{so} \quad 7 + 5 = 12
\]

4. Substitute back into the expression:
\[
[−2 − 12] − (−5) − 5
\]

5. Now simplify inside the brackets:
\[
−2 − 12 = −14
\]

6. Substitute back:
\[
[−14] − (−5) − 5
\]

7. Now handle the negative:
\[
−14 + 5 − 5
\]

8. Combine \(−14 + 5\):
\[
−14 + 5 = −9
\]

9. Finally, subtract \(5\):
\[
−9 − 5 = −14
\]

Thus, the simplified expression is:
\[
\boxed{−14}
\]