Operator Precedence in formula field

UPDATE: This issue has been officially acknoledged as an issue. You can track the progress here: https://success.salesforce.com/issues_view?Id=a1p3A000001YpUV

Currently (early 2020), Salesforce formula operator precedence reverses (*,/) with (^). In normal applications, the exponents will be evaluated first, but in Salesforce formulas, the multiplication (or division) operators are evaluated before exponents.

Users must use parentheses to work around this non-standard interpretation of mathematical expressions.

I tried 6 different combinations of operator sequences on the same four numbers, and 4/6 failed. Here are the results of my test:

> ---------------------------------------------
> DISCREPANCY!!!!
>  * MathOperatorTest2__c
>    - Salesforce  [96549157373046880]
>    - Interpreted [9886633717]
>    - Formula is  [2 + 5 * 7 ^ 11]
> ---------------
Javascript> 2 + (5 * 7) ** 11
96549157373046880

Javascript> 2 + 5 * 7 ** 11
9886633717

> ---------------------------------------------
> DISCREPANCY!!!!
>  * MathOperatorTest3__c
>    - Salesforce  [10000011]
>    - Interpreted [156261]
>    - Formula is  [2 * 5 ^ 7 + 11]
> ---------------
Javascript> (2 * 5) ** 7 + 11
10000011

Javascript> 2 * 5 ** 7 + 11
156261

> ---------------------------------------------
> DISCREPANCY!!!!
>  * MathOperatorTest4__c
>    - Salesforce  [6.617444900424221e+53]
>    - Interpreted [859377]
>    - Formula is  [2 + 5 ^ 7 * 11]
> ---------------
Javascript> 2 + 5 ** (7 * 11)
6.617444900424221e+53

Javascript> 2 + 5 ** 7 * 11
859377

> ---------------------------------------------
> DISCREPANCY!!!!
>  * MathOperatorTest6__c
>    - Salesforce  [34359738379]
>    - Interpreted [235]
>    - Formula is  [2 ^ 5 * 7 + 11]
> ---------------
Javascript> 2 ** (5 * 7) + 11
34359738379

Javascript> 2 ** 5 * 7 + 11
235

Quote from the Trailhead Advanced Formulas module

You can add (+), subtract (-), multiply (*), or divide (/) numerical values. You can also use exponentiation (^) in formulas. These operators work just like they do on a calculator. Formulas follow the order of operations, and you can group operations in parentheses.

As said in this quote, the formulas are evaluated as if they are wrote in a calculator, that means evaluated from left to right

Try your formula on this online calculator without any parentheses you'll get 16

The definition of ^ is not of exponent in the apex guide. It is mentioned as "Bitwise exclusive OR operator. Exclusive ORs each bit in x with the corresponding bit in y so that the result bit is set to 1 if exactly one of the bits is set to 1 and the other bit is set to"

For doing exponent, you can use the pow function. Eg:

Decimal myDecimal = 4; 
Decimal powDec = myDecimal.pow(2); 
system.assertEquals(powDec, 16);

Below is the snapshot of Exponent Operator from Apex Guide: