Given n is an positive integer, I came across $-2^n$ and I was wondering if this is equal to
- case (1): $2^n$ for even values of n, and $-(2^n)$ for odd values of n
- or case (2): $-2^n$, no matter what value of n is
What is the correct notation for negative of $2^n$? $-2^n$ or $-(2^n)$, if I am looking to express negative of $2^n$? Is there any standard or widely accepted convention or notation for this? I looked into ISO 31-11 and ISO 80000-2 but couldn't understand.
Case $(1)$ just amounts to "do you include the negative and hence use $(-2)^n$"?
This is obviously not the case. How does one handle expressions of the type, say,
$$10 - 2^n$$
In this sense, Case $(2)$'s interpretation is clearly used:
$$10-2^2 = 10-4=6 \qquad 10 - 2^3 = 10-8=2$$
Why should the convention differ if $10$ were replaced with $0$ instead, and hence become more compactly written as $-2^n$ (or arguably less ambiguously as $-(2^n)$)?
$-2^n$ is perfectly acceptable notation, and unambiguous (follow the order of operations), but for some a bit confusing. Those wanting to avoid it are welcome to write $(-1)(2^n)$ or any other such notation of their preference.