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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If 12x is odd and x is an integer, what is the value of x12?  Question banks Downloads My Bookmarks Reviews Important topics
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If 12x is odd and x is an integer, what is the value of x12? [#permalink]
Expert's post 00:00

Question Stats: 84% (00:33) correct 15% (00:24) wrong based on 19 sessions
If $$12^x$$ is odd and x is an integer, what is the value of $$x^{12}$$?

[Reveal] Spoiler: OA
0

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Sandy
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Re: If 12x is odd and x is an integer, what is the value of x12? [#permalink]
12^x is an odd, then x = 0. the result of x^12 = 0

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Re: If 12x is odd and x is an integer, what is the value of x12? [#permalink]
sandy wrote:
If $$12^x$$ is odd and x is an integer, what is the value of $$x^{12}$$?

[Reveal] Spoiler: OA
0

Actually
Rules: Any non-zero number to the 0th power is equal to 1, and 1 is an odd number.
Like: $$12^0$$ = 1
Same as: $$(-12)^0$$ = 1 ; $$(1001)^0$$ = 1, $$(-1312)^0$$ = 1 and so on. So here x=0 which yield odd number 1.

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Re: If 12x is odd and x is an integer, what is the value of x12? [#permalink]
First ask yourself, is there ever a value for which 12^x is odd?

At first it feels like, no, there isn't. Because no matter how many times you multiply an even number by itself it'll always be even (remembering that negative exponents usually create fractions, which are neither odd nor even).

UNLESS you remember that "x" is an integer. And "0" is an integer.

So, is there an integer value for which 12^x is odd?

Yes, 12^0 = 1. And 1 is an odd number. So, x=0, and 0^12 = 0. 0 is your answer.

The other tricky thing to remember here is that if you get too excited and go "12^0=1", you might forget what you're solving for an go "oh! x=1!". NOPE. Remember the question that you're answering; it's right in front of you, so you can double check what the question is that you're answering and make sure you're answering it  Re: If 12x is odd and x is an integer, what is the value of x12?   [#permalink] 30 May 2020, 12:09
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