$$2 ÷ 2 ÷ 2 = (2 ÷ 2) ÷ 2 \ \ \text{OR}\ \ 2 ÷ (2 ÷ 2) ?$$
Is there any standard rule which is world wide accepted for solving this type of expressions? If I process the expression from left to right then I will get $\dfrac12$. But if I process it from right to left then I get $\dfrac21$, that is $2$.
It might be that it is in invalid expression. But these type of questions are usualy asked in India's exams. E.g. the 82$^{th}$ question of SBI Clerk Exam (Held on 06-07-2008) was:
$$82.Q:\ \ \ \ \ \ \ \ \ \ \ 14400÷64÷9=?$$
The answer given was $25$. They appear to assume the order of execution from left to right.
So is the standard rule is to execute the order of operations is from left to right?
$$2 ÷ 2 ÷ 2 = 2 \cdot \frac{1}{2} \cdot \frac{1}{2} $$
Also in multiplication and division you have to go left to right then if you have addition and substraction you also have to go from left to right. Also if you have exponentiation you do that first and if you have brackets you have to do what is inside the brackets, before everything else.
Howewer when you have function composition, and exponentiation you go from right to left. For example:
$$f \circ g |_{x} = f(g(x))$$ so you first apply $g$ to $x$ and then you apply $f$ to the result of $g(x)$. When you have exponentiation: $$a^b = a \uparrow b$$ $$a^{b^c} = a \uparrow b \uparrow c$$ In the last case you also go from right to left. So: $$\left(a^b\right)^c\neq a^{(b^c)}$$