Order of operation for **

Question

I want to know why does the following happen. The code below evaluates right side 1**3 first then 2**1

2**1**3 has the value of 2

However, for the below code left side 7//3 is evaluated first then 2*3. Finally 1+6-1=6.

1+7//3*3-1 has the value of 6

Answer 1

Take a look at the documentation of operator precedence. Although multiplication * and floor division // have the same precedence, take note of this part:

Operators in the same box group left to right (except for exponentiation, which groups from right to left).

For the convention of 2¹³ being evaluated right-associative, see cross-site dupe on the math stackexchange site What is the order when doing x^yz and why?

To put it simply, since the left-associative version (x^y)^z would just equal x^y*z, it's not useful to have another (worse) notation for the same thing, so exponentiation should be right associative.

Answer 2

Almost all operators in Python (that share the same precedence) have left-to-right associativity. For example:

1 / 2 / 3   ≡   (1 / 2) / 3

One exception is the exponent operator which is right-to-left associativity:

2 ** 3 ** 4   ≡   2 ** (3 ** 4)

That's just the way the language is defined, matching mathematical notation where abc ≡ a(bc).

If it were (ab)c, that would just be abc.