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Re: Z^n = 1, What is the value of Z? 1. n is a nonzero integer [#permalink]

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13 Sep 2013, 07:32

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(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.

Re: If z^n = 1, what is the value of z? [#permalink]

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09 Sep 2015, 06:50

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This exponent rule 'concept' is something of a classic in the realm of standardized testing - it serves as a relatively simple way to assess a Test Taker's 'thoroughness of understanding' on a specific concept:

Here, the concept is "using exponent rules, and one number raised to one exponent, how many different ways can you get to the number 1?"

The first ('obvious') answer is "1 raised to any power = 1"

eg. 1^2, 1^50, 1^(-3), etc.

There are OTHER possibilities though. If your base is -1, then any EVEN exponent will lead us to a total of 1...

eg. (-1)^2, (-1)^4, (-1)^(-2), etc.

Finally, raising any number to the '0 power' will also give us a total of 1...

eg. 1^0, 537^0, (-13)^0, etc.

When dealing with this specific situation, it's important to pay careful attention to the information that you're given. What do you really know about the 'base' and the 'power' involved? If you don't know anything, then you have to consider all of the above possibilities.