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# What is the last digit 3^{3^3} ? * 1 * 3 * 6 * 7 * 9

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Senior Manager
Joined: 05 Oct 2008
Posts: 272
Followers: 3

Kudos [?]: 120 [0], given: 22

What is the last digit 3^{3^3} ? * 1 * 3 * 6 * 7 * 9 [#permalink]  18 Oct 2008, 23:44
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What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9
VP
Joined: 17 Jun 2008
Posts: 1404
Followers: 8

Kudos [?]: 153 [0], given: 0

Re: Exponents [#permalink]  18 Oct 2008, 23:50
study wrote:
What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9

3^1=3
3^2=9
3^3=27
3^4=81
3^5=*3
3^6=*9

this pattern repeats every 4 times !!!hence here 3^27 => at 3 ^24 we get 1 as ;last digit ,hence at 27 we get 7 as last digit

IMO D
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Senior Manager
Joined: 05 Oct 2008
Posts: 272
Followers: 3

Kudos [?]: 120 [0], given: 22

Re: Exponents [#permalink]  19 Oct 2008, 00:02
isn't $$3^{3^3}$$ equal to 3^3^3
meaning 27^3
then 27*27*27 gives 3 as the last digit..

can someone reinterpret 3^{3^3}
SVP
Joined: 05 Jul 2006
Posts: 1518
Followers: 5

Kudos [?]: 118 [0], given: 39

Re: Exponents [#permalink]  19 Oct 2008, 09:33
study wrote:
What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9

3^27 =

3^0 = 1

3^1 =3
3^2 = 9

3^3 = 27

3^4 = 81

27/4 = 24 and 3 is the remainder , then we have this units digit sequence (1,3,9)

9 IS THE UNIT'S DIGIT TO ME
VP
Joined: 30 Jun 2008
Posts: 1046
Followers: 11

Kudos [?]: 349 [0], given: 1

Re: Exponents [#permalink]  19 Oct 2008, 09:46
study wrote:
What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9

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Re: Exponents   [#permalink] 19 Oct 2008, 09:46
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