Re: Weird Exponent Question : GMAT Quantitative Section
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Re: Weird Exponent Question

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Re: Weird Exponent Question [#permalink]

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New post 01 Jun 2010, 16:07
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If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
\(a^m^n=a^{(m^n)}\) and not \((a^m)^n\), (by the way \((a^m)^n=a^{mn}\)).

So \(3^{3^3}=3^{(3^3)}=3^{27}\)

Cycle of 3 in power is 4. The units digit of \(3^{27}\) is the same as for \(3^3\), which is \(7\) (27=4*6+3).

Check Number Theory chapter of the Math Book for more on this issue (link in my signature).

Hope it helps.
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Re: Weird Exponent Question [#permalink]

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New post 04 Jun 2010, 12:00
Bunuel wrote:
If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
\(a^m^n=a^{(m^n)}\) and not \((a^m)^n\), (by the way \((a^m)^n=a^{mn}\)).

So \(3^{3^3}=3^{(3^3)}=3^{27}\)

Cycle of 3 in power is 4. The units digit of \(3^{27}\) is the same as for \(3^3\), which is \(7\) (27=4*6+3).

Check Number Theory chapter of the Math Book for more on this issue (link in my signature).

Hope it helps.


I confused the stacked symbols, that is something I would have got wrong on a future question!
Re: Weird Exponent Question   [#permalink] 04 Jun 2010, 12:00
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