Excel calculating exponential of negative number

Question

Using Excel 2010 I get (-8)^(1/3)=-2 but cannot calculate (-8)^(2/3)

The later returns #NUM! while mathematically I see it as (-8)^(1/3)^(2)=4 or (-8)^2^(1/3)=4

Can someone give me some insight?

Answer 1

This is intriguing.

Why can Excel find (-8)^(1/3) but not (-8)^(2/3) ?

And to make matter worse this also fails =(-8)^0.33333333333333  (14 decimals)

while this works                                     =(-8)^0.333333333333333 (15 decimals)

Perhaps someone on the Excel team can explain the algorithm used

Anyway here are a couple of workarounds

best wishes

Answer 2

Thanks for your input, Bernard Liengme

For the issue with the number of decimals, from my point of view, Excel rounded the one with 15 decimals off to 1/3, then the calculation returns the cube root of -8 which is -2 (we recall here the maths applied to calculate power of 1/n with n odd).

On the other hand the one with 14 decimal is left to be a decimal number, hence the result of the formula is an imaginary number which can't be calculated by the ^ operator.

Those are my guess, left to some experts to confirm.

What most intriguing to me is that Excel cannot return the m/n power if m is not 1. Does it means it has a test to tell in which case the exponent is rounded off, and only 1/n passes that test?

Best regards,

Answer 3

You may get some insight from below link:

http://mathforum.org/library/drmath/view/62979.html

Regards,

Amit Tandon

www.globaliconnect.com

Answer 4

Hi Dana,

Thank you very much for your reply, especially for the interesting formula and the way Excel's interpreter reads formula.

When I said =(-8)^(1/3)^(2) I really meant ((-8)^(1/3))^(2)

To me it seems inconsistent when =POWER(-8;1/3) is able to get the true and real root of the equation x^3=-8 while =POWER(-8;2/3) failed to get the square of that x.

In other words the fact that =((-8)^(1/3))^2 and =((-8)^(2*1/3)) don't give the same result irritated me, because mathematically they do. I'll much appreciate if you could give me an idea about the reason behind this inconsistency.

Best regards,