Question

How do you evaluate `-5^ { 2} + 9`?

Answer 1

I believe the correct order of operations should result in:
`color(white)("XXX")color(red)(-16)`

Explanation:

The main difficulty is in deciding if `-5^2`
should be evaluated as `-5^2=(-5)^2`
or as `color(white)("xxxxxxxxxxxxxx")-5^2=-(5^2)`

I believe the second is the correct interpretation.

If we imagine a `0` placed in front of this:
`color(white)("XXX")-5^2=0-5^2`
then the minus sing is clearly a subtraction operation with a lower precedence than exponentiation.

Reading it this way:
`color(white)("XXX")-5^2+9`

`color(white)("XXXXX")=0-5^2+9`

`color(white)("XXXXXX")=0-(5^2)+9`

`color(white)("XXXXXX")=0-25 +9`

then performing equivalent precedence operations from left to right
`color(white)("XXXXXX")=(0-25)+9`

`color(white)("XXXXXX")=-25+9`

`color(white)("XXXXXX")=-16`