Exponents: If z^n = 1, what is the value of z ?

II wrote:If z^n = 1, what is the value of z ?

(1) n is a nonzero integer
(2) z > 0

Can you please elaborate on your logic/thinking ?

Thanks.

Not completely sure but here goes: Ans A

St 1) z^n = 1 therefore z = 0 as 0 to any power = 1. (Suff)

St2) 1 ^9 = 1; and 3 ^0 - 1 hence not sufficient

Here goes the logic.
1. anything raised by power zero is one
2. one raised to power anything is one

II wrote:If z^n = 1, what is the value of z ?

(1) n is a nonzero integer
(2) z > 0

Can you please elaborate on your logic/thinking ?

Thanks.

There is tremendous debate in the mathematical community about Zero ^ Zero. Some think it is defined, some think it isnt. Since this question is being asked on the GMAT, I am inclined to go with the exception to the rule.

Anything to the power Zero = 1 ..................( Except when Anything = Zero)

Statement 1 tells us that N is not equal to zero. Since Z^N = 1, we can infer that Z = 1.

Sufficient (Therefore eliminate B /C and E as possible answers)

Statement 2 is now telling us unequivocally that z CANNOT be Zero. This doesnt give us a value for Z though.

I would be very interested in seeing what the QA is, since this will tell us whether the quirky exception is being tested or being ignored.

My answer is A.

Logic already explained by others, my vote goes to A.

Z could be positive and negative, so I'm going with C

jz95104 wrote:Z could be positive and negative, so I'm going with C

Bingo!

We have to remember that -1 raised to an even exponent will also give us a value of +1.

So, based on (1) alone, z could equal +/- 1. Once we know that z is positive, we know for sure that z is +1.

So in summary:

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

(1) n is a nonzero integer
(2) z > 0

Statement (1): n is a non-zero integer
z^n = 1. So n could be any postive/negative or odd/even number.
Recall that an even exponent can have 2 bases:
2^2 = 4
(-2)^2 = 4
So in our case z could be 1 or z could be -1. INSUFF. Remove AD from our possible answer list.

Statement (2): z > 0
This tells us nothing about n ... so INSUFF to say obtain a value for z.

(1) and (2)
Statement 1: this gave us a value of -1 and 1
Statement 2: this gave us 1, 2, 3, 4, ... (any value of z > 0).
"1" appears in both lists ... so (1) and (2) together are SUFF to solve for z.
Answer is C.

Does anyone else have any other comments or easier approach to this ?

Thanks.
II.