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# Re: Weird Exponent Question

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Math Expert
Joined: 02 Sep 2009
Posts: 42286

Kudos [?]: 132976 [2], given: 12391

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01 Jun 2010, 17:07
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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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Kudos [?]: 132976 [2], given: 12391

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Joined: 03 Feb 2010
Posts: 181

Kudos [?]: 30 [0], given: 34

Concentration: Strategy
Schools: Northwestern (Kellogg) - Class of 2014
WE: Marketing (Computer Hardware)

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04 Jun 2010, 13:00
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!

Kudos [?]: 30 [0], given: 34

Re: Weird Exponent Question   [#permalink] 04 Jun 2010, 13:00
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