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Higher Precedence
By Ed Zobel on February 19, 1998:

Dear Mathematician,

What has higher precedence, the negative, or opposite, sign unary operator or the raise to a power operation?


To be exact: Is -22 equal to -4 (giving the power higher precedence) or +4 (giving the negative sign higher precedence)?

Some calculators, notably the TI graphics line, will return -4, but others, notably SHARP scientific calulators, will return +4.


Personally, I am rooting for the negative sign as having the higher precedence, but I can handle the truth if that is not so.

A lot of my high school math students want to know also.

Ed Zobel

By Anonymous:

Dear Ed,

I believe the answer to your question lies in the idea that when a calculator, such as a Sharp calculator, changes the sign of a number with the +/- key it places that number in brackets with its sign. Raising to a power is of a higher precedence than the negation of a number, since the negation is only multiplication by negative 1.

e.g. - 22 = - 4, while (-2)2 = 4.

Perhaps, the calculator manual might be more informative.

Regards,

Del