Results discrepancy Excel vs. TI Calculator

Well:

Formula:

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works

According to this (https://support.office.com/en-us/art...rs=en-US&ad=US ) negation in Excel has higher precedence than exponentiation. So, in the expression -(-5)^2, Excel evaluates what is inside the parentheses first (yielding --5^2), performs the negation (5^2), then the exponentiation (25). Your calculator (like my Casio calculator) places negation after exponentiation, yielding the -25 that you see there. To further muddy the water, VBA uses the same order of operations as your calculator (exponentiation has higher precedence than negation). Pull up the VBE (alt-F11) and in the immediate window enter debug.print -(-5)^2 and it will output -25 like your calculator (help file for operator precedence in VBA: https://docs.microsoft.com/en-us/dot...tor-precedence ).

Wikipedia has a short entry on this: https://en.wikipedia.org/wiki/Order_...ons#Exceptions

In summary -- you, the programmer, will need to be aware of how Excel (or whatever programming language you choose to use) handles the ambiguity in cases like -a^b -- and when it conforms to your expected PEMDAS and when it differs.

Considering that Excel is over 30 years old, I doubt that anyone today recalls why they decided to do this. I would hypothesize that, like the "year 1900 as leap year but it really isn't" bug (https://support.microsoft.com/en-us/...is-a-leap-year ), the earliest spreadsheets (Visicalc or Lotus 1,2,3) chose this convention, and Microsoft Excel had to adopt this convention in order to be compatible with what was then the dominant spreadsheet. In a kind of "founder effect", once the earliest dominant spreadsheet had decided to use this convention, all others followed suit. Once established, compatibility issues prevented changing to a different convention. Of course, this only pushes the question of "why" back to those earliest spreadsheets, and doesn't really answer the question.

@ MrShorty

I am still not getting this.

-(-5^2) = -25

This looks to me like proper application of PEMDAS and yields the correct answer.

What am I missing?

Very interesting - if the exponent is on the 5 rather than the close parenthesis it works

Formula:

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Yes.

I guess don't see a problem here.

It appears to be fundamental algebra and proper formula setup ... ie solve what's inside the () first. Excel is quite consistent in honoring this from what I have observed.

Perhaps PEMDAS needs to be amended ... ()PEMDAS ...

FlameRetired -- Correct -(-5^2) correctly evaluates to -25 -- even in Excel. But that was not the exact example the OP used. Note the different placement of the closing parenthesis:

-(-5^2)=-25 -- yours
-(-5)^2=+25 -- OP's

Ultimately this boils down to how to interpret the vague expression -a^2. When expressed like this, do we mean -1*a^2 (like xladept expands the expression, and the way most programming languages and algebra teachers would describe it) where we are assuming the leading - sign is indicating a multiplication by -1. Or do we mean (-a)^2 (which is how Excel [incorrectly??] interprets the problem) where the leading - sign is an integral part of the number.

Note the different placement of the closing parenthesis:

-(-5^2)=-25 -- yours
-(-5)^2=+25 -- OP's

Noted. It just seemed to me to be more "mathematically correct". It just looked like Excel actually gets it right and TI gets it "buoɹʍ".