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

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If z^n = 1, what is the value of z? [#permalink] New post 29 Jun 2012, 04:50
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If z^n = 1, what is the value of z?

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

Zero raised to any power is zero and any number raised to the power of 0 equals one?
Is that the rule of it is reversed?
[Reveal] Spoiler: OA

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Re: If z^n = 1, what is the value of z? [#permalink] New post 29 Jun 2012, 04:59
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Stiv wrote:
If z^n = 1, what is the value of z?

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

Zero raised to any power is zero and any number raised to the power of 0 equals one?
Is that the rule of it is reversed?


I'm not sure understand the red part in your post above.

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

(1) n is a non zero integer --> 1^{any \ integer}=1 and also (-1)^{even}=1, so z can be 1 or -1. Not sufficient.

(2) z > 0 --> any nonzero number to the power of 0 is 1, so if n=0 then z can be any non-zero number (any positive number in our case as given that z>0). Not sufficient.

(1)+(2) n is a nonzero integer and z>0 implies that z can equal to 1 only. Sufficient.

Answer: C.

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PS questions on exponents: search.php?search_id=tag&tag_id=60

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Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Re: If z^n = 1, what is the value of z? [#permalink] New post 04 Feb 2013, 19:50
Statement 1 is insufficient here are some examples

For z^n = 1, and n being a non zero integer, there are 3 possible ways.
a. 1^1 = 1
b. 1^- 1 = 1
c. - 1^2 = 1

Statement 1 not conclusive. Z could be 1 or -1.

Statement 2: z > 0.

Examples 2^0 = 1 , 3^0 = 1

not sufficient

together n can't be 0 and Z has to be greater than 1 only one case

1^1 is the answer sufficient. Answer Choice C
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Re: If z^n = 1, what is the value of z?   [#permalink] 04 Feb 2013, 19:50
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