ZERO raised to power ZERO = what...? is it ONE..?

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girishbtg: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Mon Sep 20, 2010 12:51 am

by girishbtg » Mon Oct 25, 2010 4:56 am

ZERO raised to power ZERO = what...? is it ONE..?

isn't equal to INFINITE... am in confusion.. please explain...

Thanks

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 25, 2010 4:56 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Oct 25, 2010 5:35 am

girishbtg wrote:ZERO raised to power ZERO = what...? is it ONE..?

isn't equal to INFINITE... am in confusion.. please explain...

Thanks

Hi there,

SOMETIMES it is useful to CONSIDER that zero raised to the power zero is one (for instance in some areas of Combinatorics) but, in Mathematics in general (therefore in the quant section of the GMAT), without any (local and) explicit consideration,

Zero raised to power Zero is UNDEFINED.

(That means: there is no proper way to DEFINE this expression without "leaving room for contradictions".)

That means that you cannot be asked to calculate its value. Simple as that.

Regards,
Fabio.

P.S.1: every real number, EXCEPT ZERO, raised to the power zero is equal to one.

P.S.2: infinite is not a (real) number, infinite is a symbol. And although it is possible in Mathematics, to "adjoint" the infinity to the real numbers (the so called "extended real number line"), this is far from GMAT, so out-of-our-scope. (And even doing so, zero raised to the power zero is still undefined.)

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Oct 25, 2010 5:54 am

girishbtg wrote:ZERO raised to power ZERO = what...? is it ONE..?

isn't equal to INFINITE... am in confusion.. please explain...

Thanks

This is a very old debated topic in mathematics.
Best value for zero raised to the power zero depends upon the context. Sometimes it is taken as 1 and sometimes as indeterminate (not infinity). Consider the following cases,
(1) In combinatorial or set theoretic approach zero raised to the power zero is equal to 1.
(2) In differential calculus and limit theory most of the time zero raised to the power zero is indeterminate.

For further information, https://en.wikipedia.org/wiki/Exponentia ... zero_power

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Oct 25, 2010 2:56 pm

You will never need to know anything about 0^0 on the GMAT, by the way; there will simply never be a question where such an expression is even allowed.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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girishbtg: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Mon Sep 20, 2010 12:51 am

by girishbtg » Mon Oct 25, 2010 10:39 pm

Ian Stewart wrote:You will never need to know anything about 0^0 on the GMAT, by the way; there will simply never be a question where such an expression is even allowed.

Experts,

Am showing the ques.. where i faced this dilemma...

You can see that this concept is needed in GMAT...

and acc to GMAC , ZERO raised to power ZERO =1

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Oct 25, 2010 11:15 pm

girishbtg wrote: Experts,

Am showing the ques.. where i faced this dilemma...

You can see that this concept is needed in GMAT...

and acc to GMAC , ZERO raised to power ZERO =1

If Z^n = 1, what is the value of Z?

(1) n is a nonzero integer.
(2) Z > 0

We don't need the concept of zero raised to the power zero.
Given that, Z^n = 1

Statement 1: n is a nonzero integer
Implies,
(1) Z = 1 or -1 for n even
or
(2) Z = 1 for n odd

Not sufficient.

Statement 2: Z > 0. No information about n. Thus Z may be equal to any positive number when n = 0 and Z may be equal to 1 when n is any positive integer. For both of the cases Z^n = 1.

Not sufficient.

1 & 2 Together: Z = 1 as Z > 0.

The correct answer is C.

Last edited by Rahul@gurome on Mon Oct 25, 2010 11:28 pm, edited 1 time in total.

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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
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girishbtg: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Mon Sep 20, 2010 12:51 am

by girishbtg » Mon Oct 25, 2010 11:20 pm

Rahul@gurome wrote:
girishbtg wrote: Experts,

Am showing the ques.. where i faced this dilemma...

You can see that this concept is needed in GMAT...

and acc to GMAC , ZERO raised to power ZERO =1

If Z^n = 1, what is the value of Z?

(1) n is a nonzero integer.
(2) Z > 0
We don't need the concept of zero raised to the power zero.
Given that, Z^n = 1

Statement 1: n is a nonzero integer => Z must be equal to 1

Sufficient.

Statement 2: Z > 0. No information about n. Thus Z may be equal to any positive number when n = 0 and Z may be equal to 1 when n icddds any positive integer. For both of the cases Z^n = 1.

Not sufficient.

The correct answer is A.

NO......

As as u can see that even myself put ans as A..
but it's WRONg.. that why i put this ques here as doubt

Ans is C

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Oct 25, 2010 11:30 pm

Sorry.
My mistake. Didn't considered the -1.

Edited the reply.

Thanks.

Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Oct 26, 2010 6:39 am

girishbtg wrote:
Ian Stewart wrote:You will never need to know anything about 0^0 on the GMAT, by the way; there will simply never be a question where such an expression is even allowed.
Experts,

Am showing the ques.. where i faced this dilemma...

You can see that this concept is needed in GMAT...

You do not need to use any property of 0^0 in the question you posted. In fact they go to some length to rule out the possibility that z^n is equal to 0^0. What I said above was true: you don't need to know anything about 0^0 for the GMAT.

In the question you posted, you need to consider the possibility that the base is -1. That's why the answer is C; it has nothing to do with 0^0.

girishbtg wrote: and acc to GMAC , ZERO raised to power ZERO =1

No, that is simply not true. GMAC is not free to invent their own mathematics. The GMAT uses the same math that everyone else does, and in the real world of math, there is no universally accepted definition of 0^0.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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