# GingerAle

 Username GingerAle Score 1914 Membership Stats Questions 2 Answers 601

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### Happy Birthday Hectictar

GingerAle  Oct 14, 2018
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### Hectictar! A Year of Excellence!

GingerAle  Feb 7, 2018
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off-topic
GingerAle  Jan 8, 2018
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### That’s one way to get a new user name, Miranda.

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GingerAle  Aug 6, 2017
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This debate seems perpetual. The issue returns at least once every school year.

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Another reason I prefer the rule "only use the item immediatley adjacent to the operator as the operand" is that we can use a similar rule for exponents. In the case of exponents, the rule would be "only the item immediately preceding the caret is the base."

4^2^3

Should  4^2^3  be  4^(2^3)  or  should it be  (4^2)^3   ?

If we just stick with the left-to-right rule, we would get

4^2^3  =  16^3  =  4096

Note that the web2.0calc calculator resolves this from the left to right or ascending order, where the resultant product becomes the BASE of the next exponent.  This operation is easy to see in the display above the calculator.  This is the only exception to the hierarchical order of operations. The reason for this is probably because the standard product of exponents to a base is well more common in physics and engineering than conventional stacked powers.

If we use the rule "only the item immediately preceding the caret is the base," we would get

4^2^3  =  4^8  =  65536

Here, WolframAlpha says the answer is  65536:

Wolfram follows the (official) stacked power convention, where stacked powers are (exponentially) multiplied from the right to left (from the top down), and the resultant product becomes the EXPONENT to the base number. Generally, stacked power and power-towers are used in advanced, theoretical mathematics.

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According to the answer there,  a/bc  means  a/(bc)  which goes against my idea.

Hmm, I don't like that! But I guess it is the case. Though I still think  1/4(3)  =  3/4

For a/bc, the convention will equal a/(bc)

Implicit multiplication of variables takes precedents over division – a noted exception, dating back to the late 1960s, to the normal convention of mathematical hierarchy. Herr Massow’s calculator is the only one I know of that that does this, and it’s probably because it allows the use of variables. (Comments from LancelotLink –2015)

Pasting a=20;b=2;c=5; a/(b)(c) in the calculator will result in (2).

Pasting 20/2*5 in the calculator will result in (50)

Note that pasting 20/(2)(5) will result in (2),  but pasting this 20/(2)*(5) will result in (50). The parenthesis without an operator between them triggers the variable precedents.

Note also, that the convention for precedents of variables multiplication applies only to the first two variables.

Posts related to hierarchy-order of operations:

https://web2.0calc.com/questions/help-with-pemdas

https://web2.0calc.com/questions/4-2-x-2-2-x-56#r8

GA

Aug 3, 2019