PEMDAS in negative base

Question

Hi,

I was going through the mgmat guides for quant and came across this concept for the applicability of pemdas rule in negative bases.

Basically according to the book:

-2^4 = -1* (2^4)= -16 and,
(-2)^4 = (-1^4) * (2^4) = 16

Just wanted to confirm whether this is applicable or not in the gmat as I haven't seen this in any other book.

Thank you very much in advance

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Kinshook · Answer

Hi  ShivanshAggarwal 
The concept mentioned in MGMAT Quant guide is universally applicable, and there is no ambiguity in it.

Hope it helps!

IanStewart · Answer

GMAT math is identical to math everywhere else, and the rule you cite is correct, whether you're doing math on the GMAT or math in a university class. If there are no brackets, exponents apply exclusively to the number or letter they are immediately attached to, and to nothing else. So if you see

ab^4

then the exponent applies only to b, and not to ab -- we could correctly rewrite this as  (a)(b^4) . The situation you cite is identical. When you see  -2^4  that really means  (-1)(2^4) , and again, the exponent only applies to the "2", and not to the "-1". It's only by using brackets, so by writing  (ab)^4  or  (-2)^4 , that the exponent would apply to more than one number or letter.

We do encounter this situation all the time in GMAT math (probably often without even realizing it, which I expect is why Kinshook above says he hasn't seen it). When you see something like

a - b^2

the exponent "2" applies only to "b", and not to "-b".

Russ19 · Answer

IanStewart  Could you please explain the line( the exponent "2" applies only to "b", and not to "-b". ) a bit?

sa119 · Answer

Got it, thank you Kinshook and Ian!

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IanStewart · Answer

I'm not sure I can add anything to what I said above. If you see

-b^2

then we are squaring b alone. We are not squaring "-b". So the result will automatically be negative, or zero in the case when b = 0.

On the other hand, if you see

(-b)^2

then we are squaring "-b". This will equal b^2, and will automatically be positive, or zero in the case when b = 0.

unraveled · Answer

PEMDAS is American equivalent of BODMAS(British English). So whatever you have learnt in BODMAS is applicable in PEMDAS as well, just that M and D exchange their places - they are of equal level and rank. By default '-2^4' is '-1* (2^4)' .

Otherwise every Math concept is universal without any exception.

freedom128 · Answer

The pemdas and other math principles are universal, so this will also apply to gmat test. Good luck

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PEMDAS in negative base

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