Wolfram alpha is giving inconsistent results to this problem:
When I enter:
16÷2( 8-3(4-2) )+1 the result is 17.
When I enter:
16÷2[ 8-3(4-2) ]+1 the result is 5.
and
16÷2*[ 8-3(4-2) ]+1 brings us back to 17.
I attribute the third case to the explicit multiplication, meaning the division occurs before the 2 is distributed over the bracket. But should the first two not yield the same result?
NOTE: The original problem was intentionally ambiguous, with the purpose of showing the dangers of the ÷ operator, so let's not talk about that.
It has nothing to do with $÷ $ at all. It is all about how Alpha interprets "$2*[..]$" vs "$2[..]$".
The square bracket means a function application. Alpha gives precedence to $f[x]$ (expression $f$ applied to expression $x$, or $f(x)$) over other arithmetic operators. But since $2$ is not a function, $2[\cdots]$ is interpreted as $(2\times \cdots)$ before the rest of the expression.
You can easily see the difference is a simpler example: $16 ÷ 2[3]$ is $$\frac{16}{2 \times 3}$$ but $16 ÷ 2*[3]$ is $$\frac{16}{2}\times 3.$$