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

Hi Amit Tandon,

That's an interesting site. Thank you.

It however didn't give me the answer I want, since I'm well aware that most exponentiation with decimal exponents don't give us real results. However in this particular case we have x^(1/3) and x^(2/3), with the later to me is the square of the former.

So my real concern is the inconsistency that Excel can return real number for the former but can only return complex number for the later.

Let's say I'm very curious of the algorithm used by Excel to calculate non-integer power.

Best regards,

Answer 2

I would like to confuse the situation further in that both Wolfam Alpha and Microsoft Mathematics define -8^(2/3) as -4 not 4.

Answer 3

Hi. The issue is that Excel will calculate this as:

=-4^2

16

But those programs return:

-(4)^2

-16

Here's an interesting reference

Order_of_operations

Under special cases:

... because exponentiation is right-associative in mathematics thus...

...For example, Microsoft Excel evaluates a^b^c as (a^b^)^c^, which is opposite of normally accepted convention...

Other topics like Tetration (exponentiation), "Power Towers", etc..  are all right-to-left...etc

Answer 4

RVCollins wrote:

I would like to confuse the situation further in that both Wolfam Alpha and Microsoft Mathematics define -8^(2/3) as -4 not 4.

That's because Excel parses the expression as (-8)^(2/3), whereas Wolfam Alpha parses it as -(8^(2/3)).

Some people like to argue that Excel is "wrong" and the Wolfam Alpha interpretation corresponds to mathematics.

But first, it is what it is.  And second, there is no "right" or "wrong". Excel is a progamming language, and each programming language chooses its own rules.

For example, in APL, there are no precedence rules, and operations associate right-to-left. Moreover, "*" is the exponentiation operator, not the multiplication operator. So 2*3 is 8, not 6.  And 3*2+4 is 729, not 85.  Also, 2*3 does not equal 3*2.