Negation is an operation; it's an example of a
unary operation.
No, according to the
standard order of operations, -2^4 = 16.
There is no law that prohibits a company from marketing calculators or computer software (e.g, Microsoft Excel) that use a non-standard order of operations, but I think it is silly to do so.
This reminds me of a joke I once read. How many Microsoft employees does it take to change a burnt-out lightbulb? None. Microsoft declares darkness the standard.
A standard order of operstions aids communication; if everyone follows the standard, then everyone knows what a given expression means. In the standard order of operations, the power operation takes precedence over negation.
As an example, consider the equation
-x^2 + 16 = 0.
According to the standard order of operations, x = -4 and x = 4 are solutions to this equation. According to your non-standard order of operations, x = -4i and x = 4i are solutions to this equation, which seems quite bizarre.
I applaud TI for using the standard order of operations. Maple also follows the standard order of operstions and returns -2^4 = -16.
Agreed.