Excel question

[eenglish]

When I calculate -4^-4 in Excel, I get a positive answer. When I
calculate -4^-4 on my hand held Casio Algebra FX 2.0, I get a
negative answer. This is in a home schooling test where the correct
answer is negative..

Calculating 4^-4 results in a positive answer also.

Expanation?

Thanks,

Ed

 

[GS]

(e-mail address removed) pretended :

When I calculate -4^-4 in Excel, I get a positive answer. When I
calculate -4^-4 on my hand held Casio Algebra FX 2.0, I get a
negative answer. This is in a home schooling test where the correct
answer is negative..

Calculating 4^-4 results in a positive answer also.

Expanation?

Thanks,

Ed

Try...

=-(-4^-4)

 

[GS]

Or did you mean...

=-(4^-4)

 

[Auric__]

When I calculate -4^-4 in Excel, I get a positive answer. When I
calculate -4^-4 on my hand held Casio Algebra FX 2.0, I get a
negative answer. This is in a home schooling test where the correct
answer is negative..

Calculating 4^-4 results in a positive answer also.

Expanation?

Assuming you mean (-4)^(-4), the correct answer is positive:
(-4)^(-4)
1/((-4)^4)
1/((-4)(-4)(-4)(-4))
1/((16)(16))
1/256

When the exponent (to the right of the ^ sign) is even, and the base is a
real number, then the result will *always* be positive.

As Garry pointed out, the order in which the symbols are interpreted will
greatly affect what actually happens. It looks like Excel assumes (-4)^(-4),
while your Casio and the test probably assume -(4^(-4)) (which gives a
negative result).

I'd highly suggest asking this in a math group, e.g. sci.math.

 

[MerseyBeat]

When I calculate -4^-4 in Excel, I get a positive answer. When I
calculate -4^-4 on my hand held Casio Algebra FX 2.0, I get a
negative answer. This is in a home schooling test where the correct
answer is negative..

Calculating 4^-4 results in a positive answer also.

Expanation?

Thanks,

Ed

Ed,

Here is the explanation.

The correct answer CANNOT be negative. Any number, whether positive or
negative, multiplied by itself an even number of times MUST be positive !

The home schooling exam result IS wrong. The only way it could be negative
would be if it was written as Garry suggested, -(-4^-4).

eg:

4^4 is equivalent to 1 x 4 x 4 x 4 x 4 = 256

4^-4 is equivalent to 1 / 4 x 4 x 4 x 4 = 1/256 = 0.00390625

-4^-4 is equivalent to 1 / -4 x-4 x-4 x -4 = 1/256 = 0.00390625

HTH

On the Casio Algebra FX 2.0, when you press the following buttons in this
exact sequence :
4 +/- x^y 4 +/- =
you receive a negative number ???

If so, get your money back for the Casio Algebra FX 2.0 !!! It's wrong
also.

Cheers,
MB

 

[joeu2004]

When I calculate -4^-4 in Excel, I get a positive answer.
When I calculate -4^-4 on my hand held Casio Algebra
FX 2.0, I get a negative answer. This is in a home schooling
test where the correct answer is negative.. [....]
Expanation?

In mathematics, -4^-4 is written with a superscript -4, so it is evaluated
as -(4^-4). That is how you should write it if you want the result to
conform to standard mathematics notation.

In Excel, -4^-4 is evaluated as (-4)^-4. Note that a negative number raised
to an even power is always positive.

Some people like to say that Excel is "wrong" because it does not conform to
mathematics. But really, they are two difference languages, and they have
different ordering rules, just like natural languages that might use the
same alphabet.

As long as you understand Excel's rules for the order of operations, you can
get away without using parentheses.

But in general, you should parenthesize sub-expression to ensure that they
are evaluated as you intend them to be.

You could write -(4^(-4)). However, I think it is prudent to minimize the
use parentheses in order to improve readability. Since ...^-4 can only be
interpreted one way, you can avoid the extra set of parentheses.

 

[joeu2004]

In mathematics, -4^-4 is written with a superscript -4,
so it is evaluated as -(4^-4).

I forgot to say: obviously the Casio Algebra FX 2.0 has chosen the
mathematical interpretation. (In fact, it might even display the
superscript -4. I don't know.)

There is nothing wrong with the Casio calculator. In fact, many people
insist the opposite: Excel is "wrong". As I mentioned previously: in
fact, neither is wrong.

 

[Rick Rothstein]

When I calculate -4^-4 in Excel, I get a positive answer.

When I calculate -4^-4 on my hand held Casio Algebra
FX 2.0, I get a negative answer. This is in a home
schooling test where the correct answer is negative..

I think I disagree with the answer being negative. The idea of that
calculation looks, to me, to be to raise "negative four" to the "negative
four" power. To do that on a calculator, you would enter the number 4 first,
then you would press the "plus/minus" key to change its value to "-4" in the
display, then you would press the "raise to a power" key, then you would
press the 4 key followed again by the "plus/minus" key and finish it off
with the Enter key. If you do it that way, I think your calculator will
report a positive answer.

Rick Rothstein (MVP - Excel)

 

[joeu2004]

When I calculate -4^-4 on my hand held Casio Algebra
FX 2.0, I get a negative answer. This is in a home
schooling test where the correct answer is negative..

I think I disagree with the answer being negative. [....]
To do that on a calculator, you would enter the number 4 first, then you
would press the "plus/minus" key to change its value
to "-4" in the display, then [....]

Only because you imposed your own sense of precedence on the operation.

In the language of mathematics, -4^-4 would be interpreted as -(4^-4).
There is no operator called "change sign" in mathematics. Instead, a unary
minus has the lowest precedence (among these operations, anyway) so
that -4^-4 has the same result as 0-4^-4. It is axiomatic that 0+e=e.

(In fact, if you enter =0-4^-4 into Excel, you do indeed get a negative
result.)

I'm not familiar with the Casio Algebra FX 2.0 calculator, but some
"algebraic" calculators actual permit us to enter superscript powers. And
some make a point of allowing the student to enter mathematical formulas
exactly as they appear in textbooks and evaluating according to the commonly
accepted rules of mathematics.

None of this should be misinterpreted that either precedence ordering is
"wrong" or "right". They are both right for their respective languages.