Step by step
The question
Question: work out |2 − 3²| + (−1)³.
|2 − 32| + (−1)3
1 Inside the bars
The bars work like brackets.
They come first.
Powers come before minus.
Order: ( ) → x² √ → × ÷ → + −
3² means 3 times 3.
32 = 3 × 3 = 9
That is 9.
= |2 − 9| + (−1)3
We take away more than we have.
Start at 2.
Go down 9.
We pass 0 and land on −7.
= |−7| + (−1)3
2 Absolute value
| | = how far from 0
The bars mean: how far from 0?
That is never negative.
So |−7| is 7.
= 7 + (−1)3
3 Powers
Powers come before plus.
(−1)³ means −1 times −1 times −1.
An odd number of minuses gives minus.
(−1)3 = (−1) × (−1) × (−1) = −1
That is −1.
= 7 + (−1)
4 Plus and minus
Adding a negative is the same as taking away.
+ (−) = −
So 7 + (−1) becomes 7 − 1.
= 7 − 1
7 minus 1 is 6.
= 6
So the answer is 6.
Let's look back.
First: inside the bars.
Then: absolute value.
Then: powers.
Last: plus and minus.
Answer
= 6