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Having trouble dealing with exponents with infix and postfix.

Posted on 2011-05-04
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Last Modified: 2012-05-11
So I understand that converting something like:
4 + 2 * 8 / 6 + 2
goes from left to right, so to get the postfix you throw parentheses in it based around the precedence from left to right:
( ( 4 + ( ( 2 * 8 ) / 6 ) ) + 2 )
then you get the postfix by going left to right and pulling the numbers and operators based on the right parentheses:
428*6/+2+

But what about for exponents?
3^2^1
does this go from right to left?
(3^(2^1))
If so is this the only step thats different with exponents?
Postfix?:
321^^
Then would you evaluate this the same you would with any postfix?

Then does the following evaluate to 49? For some reason I have 19 in my notes...
6342^*+5-
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Question by:Eindoofus
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Expert Comment

by:phoffric
ID: 35689826
I use left to right associativity for exponents:
     http://www.mathgoodies.com/lessons/vol7/operations_exponents.html
3^2^1
((3^2)^1) = 9

63(42^)*+5- = 63 16*+5- = 49
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Author Comment

by:Eindoofus
ID: 35689894
This follow is from:
http://en.wikipedia.org/wiki/Order_of_operations

Calculators may associate exponents to the left or to the right depending on the model. For example, the expression a ^ b ^ c on the TI-92 and TI-30XII (both Texas Instruments calculators) associates two different ways:
The TI-92 associates to the right, that is
a ^ b ^ c = a ^ (b ^ c) =  
whereas, the TI-30XII associates to the left, that is
a ^ b ^ c = (a ^ b) ^ c = (ab)c.


I could have sworn that in my class the professor said it was right to left. I don't understand how something like this has no definitive rule in mathematics?

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Accepted Solution

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phoffric earned 2000 total points
ID: 35689931
There are different standards in different countries. And Microsoft Windows XP calculator still says that  4+3*2 = 14, whereas from algebra throughout college, the answer has been 10.

Look up in your textbook what standard you are using.
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Author Comment

by:Eindoofus
ID: 35689978
So I take it that the standard only matters when going from infix to postfix?

With the following:
6342^*+5-
Is there anyway to get 19 out of that? The only thing I can pull from that is 49.
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Expert Comment

by:phoffric
ID: 35690070
Sorry, I haven't been able to come up with 19 yet.
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