Why is it that Microsoft Excel says that 8^(-1^(-8^7))) = 8 instead of 1/8?

Question

Why is it that Microsoft Excel 7 says that 8^(-1^(-8^7))) = 8 while Wolfram Alpha says it equals 1/8?
These results are the same if I substitute -2097152.0 for -8^7.
Now -1 to any power is -1. Therefore -1^(-8^7) = -1. And 8^-1=1/8.
Excel is wrong.
Try it and see!

Excel 7 is 20 years old, there have been hundreds of bugs, this likely was one of them. Stop using software from 1997. — Ramhound, Aug 29 '16 at 22:21
I'm voting to close this question as off-topic because Excel 7 (Excel 97) is from 1997, there is no possible way, for anyone to know the reason Excel 97 incorrectly calculated the specified value — Ramhound, Aug 29 '16 at 22:23
@Ramhound He's also wrong in the first place. 8^((-1)^(-8^7)) is not the same as 8^(-1^(-8^7)) to Wolfram. It is to excel; in fact, Excel is more refined than Wolfram with this calculation. — var firstName, Aug 29 '16 at 22:23
I'm voting to close this question as off-topic because 8^(-1^(-8^7))) has mismatched parentheses and is therefore an invalid expression. — DavidPostill, Aug 29 '16 at 22:43
Just clarification for potential close voters: 1) A question is not off-topic because it is about old software; that just limits how many people can answer (and this problem is not limited to Excel 7). 2) A question is not necessarily off-topic because of mismatched parentheses; that might be the answer. 3) Questions that exist only because of a typo are generally considered off-topic because they aren't really about a hardware or software problem. That appears to be the case here. Rather than create a 3rd custom close reason, DavidPostill's reason is close enough for government work. — fixer1234, Aug 29 '16 at 23:48
It turns out this has nothing to do with Excel 97. Can be replicated in Excel 20013/2016. See =8^(-1^(-8^7)) = 8 vs =8^(-(1^(-(8^7)))) = 0.125 — Brad, Aug 29 '16 at 23:57
Why does =-x^2+x for x=3 in Excel result in 12 instead of -6?, According to Excel, 4^3^2 = (4^3)^2. Is this really the standard mathematical convention for the order of exponentiation? — phuclv, Apr 16 '20 at 16:08

score 3 · Answer 1 · answered Aug 29 '16 at 22:51

3

Excel and Wolfram Alpha have difference precedence rules for parsing an expression like this involving exponentiation and unary minus.

- x ^ y

Excel treats unary minus as higher precedence and does it first, evaluating the expression as:

( - x ) ^ y

Wolfram Alpha does the exponentiation first, evaluating the expression as:

- ( x ^ y )

answered Aug 29 '16 at 22:51

Nicole Hamilton

10,023

1

Hence Excel is a poor tool to learn the basics of math. ;). – dan Aug 30 '16 at 06:54
Okay, but at least it follows the same precedence rules as C/C++. – Nicole Hamilton Aug 30 '16 at 08:54

Gary's Student · Answer 2 · 2016-08-30T14:18:50.237

The problem is that in Excel the minus sign is used to signify both the subtraction operator and the unary sign. It is easy to illustrate this. In A1 enter:

=-1^(ROW())

and copy down:

The flip/flopping positive/negative indicates that Excel sees the minus sign as a unary and treats this formula like:

=(-1)^(ROW())

Now in B1 enter:

=0-1^(-ROW())

and copy down:

The lack of flip/flopping indicates that Excel sees the minus sign as a subtraction operator and treats this formula like:

=0-(1^(-ROW()))

Of course, the user can always control the precedence by using parenthesis.

EDIT#1:

See Bill Jelen's explanation

score 1 · Answer 3 · edited Jun 12 '20 at 13:48

1

Wolfram Alpha does this:

-(1^-2097152) = -(1) = -1

8^-1 = ¹/₈

Excel, on the other hand, does this:

(-1)^-2097152 = 1

8¹ = 8

Indeed, Excel is wrong - it should exponentiate first, then negate. Try this formula: =8^(-(1^(-8^7)))

Now -1 to any power is -1

As var firstName already pointed out, that's incorrect. However, it's true that -1^N = -1 is true for any N - again, because you should exponentiate first, then negate.

edited Jun 12 '20 at 13:48

Community

1

answered Aug 29 '16 at 22:23

gronostaj

57,004

No, actually, Excel is right. That method of entry is incorrect. OP meant 8^((-1)^((-8)^7)) – var firstName Aug 29 '16 at 22:26
@varfirstName Why would it be incorrect? Standard order of operations is: exponents and roots, then multiplication and division, then addition and subtraction. So basically the Wolfram Alpha order. Excel groups (-1) first (basically 0 - 1 subtraction), then exponentiates - that's incorrect order. – gronostaj Aug 29 '16 at 22:30
if the post-calculation multiplication was intended, it would be marked by extra separating parentheses. – var firstName Aug 29 '16 at 22:34
@varfirstName "OP meant 8^((-1)^((-8)^7))". You don't know that. It's not what he wrote (in two different places). – DavidPostill Aug 29 '16 at 22:46
@gronostaj I think more properly stated is that Excel ranks negation first (unary minus), and then exponentiation, then multiplication and division, then addition and subtraction. In Excel, -1 is different from 0-1. eg: -1^2 ► 1. 0-1^2 ► -1. The first is considered a unary operator, the second a binary operator. – Ron Rosenfeld Aug 31 '16 at 12:25

var firstName · Answer 4 · 2016-08-29T22:21:55.907

0

That's incorrect. -1^2 is 1. However, -1 to any odd power is -1; that is true. Using perfectly sensible logic, you can say that 8^(-1^(-8^7)). -8 ^ 7 = -2,097,152, an even number; therefore, -1^(-2,097,152) is 1/(-1^(2,097,152)) which reduces to 1/1 or simply 1, and 8^1 is 8. Your entry to WolframAlpha is flawed in some way.

EDIT: I did the calculation on Wolfram and it turns out that you entered it wrong. You're supposed to isolate the -1 further from the base, like this:

8^( (-1)^(-8^7) )

Wolfram spit this out back at me (identical to my entry):

8^((-1)^(-8^7))

edited Aug 29 '16 at 22:21

answered Aug 29 '16 at 22:15

var firstName

1,777

1

He says that -1 to any power is -1 which is completely incorrect. – var firstName Aug 29 '16 at 22:30
No, that's completely incorrect, any number to the -1 is 1 over that number – var firstName Aug 29 '16 at 22:32
My point is, he said negative one to any power is -1, which is incorrect. (negative one being the base, in all circumstances.) – var firstName Aug 29 '16 at 22:36
Let us continue this discussion in chat. – var firstName Aug 29 '16 at 22:39
This is wrong. In math power operator has higher precedence than unary minus so -1^2 = -1, and it has right-to-left associativity so 2^3^4 = 2^(3^4). Almost all languages with power operator do follow the math rule like that. See Why is exponentiation applied right to left?, Why is exponentiation right associative? – phuclv Apr 16 '20 at 16:08

Why is it that Microsoft Excel says that 8^(-1^(-8^7))) = 8 instead of 1/8?

4 Answers4