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

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19 Oct 2008, 00:44
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What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9

Kudos [?]: 550 [0], given: 22

VP
Joined: 17 Jun 2008
Posts: 1374

Kudos [?]: 425 [0], given: 0

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19 Oct 2008, 00:50
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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Kudos [?]: 425 [0], given: 0

Senior Manager
Joined: 05 Oct 2008
Posts: 267

Kudos [?]: 550 [0], given: 22

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19 Oct 2008, 01:02
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}

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

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19 Oct 2008, 10:33
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

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VP
Joined: 30 Jun 2008
Posts: 1031

Kudos [?]: 729 [0], given: 1

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19 Oct 2008, 10:46
study wrote:
What is the last digit $$3^{3^3}$$ ?

* 1
* 3
* 6
* 7
* 9

_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 729 [0], given: 1

Re: Exponents   [#permalink] 19 Oct 2008, 10:46
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# What is the last digit 3^{3^3} ? * 1 * 3 * 6 * 7 * 9

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