Does exponent notation apply only to the base or the whole expression?

[C0nfused]

Hi
I have a small question about exponents: when we write a^x (i will write it this way but i talk about the traditional notation) this means that the base is only a? I mean that if we have ba^x or -a^x then then these are equal to b(a^x) and -(a^x) ? These are also because of the order of operations? Generally if we want a "whole expression" to be raised in a power then we have to write it in a parentheses? So for example -2^2=-4 but (-2)^2=4 ?
So we calculate this exponent and then do multiplications, divisions etc..?
Thanks

 

[mathwonk]

i agree with you. i.e. i use the notation as you have said.


one remark: if you intend also to raise your base to fractional powers, like 1/2,

then you are particularly advised that, if you are dealing with real numbers, the base should be positive, since (-1)^*1/2) is not a real number.

i.e. in ordinary calculus courses about real numbers, in first and second year in most US universities, a^x should only be used when a is positive (or zero). I.e. if you intend a^x to be a function defiend for all real numbers x, or even for all rational numbers x, then a should be positive.

 

[HallsofIvy]

Yes, it is based on "order of operations". -2²= - 2*2= -4 because exponentiation takes precedence: it is -(2)(2). (-2)²= (-2)(-2)= 4 because of the parentheses.