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M09-32

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M09-32  [#permalink]

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New post 16 Sep 2014, 00:40
2
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (00:22) correct 50% (00:23) wrong based on 136 sessions

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Re M09-32  [#permalink]

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New post 16 Sep 2014, 00:40
1
1
Official Solution:

What is the last digit of \(3^{3^3}\)?

A. 1
B. 3
C. 6
D. 7
E. 9


THEORY

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 \((a^m)^n\), which on the other hand equals to \(a^{mn}\).

So:

\((a^m)^n=a^{mn}\);

\(a^{m^n}=a^{(m^n)}\) and not \((a^m)^n\).

BACK TO THE QUESTION

According to the above: \(3^{3^3}=3^{(3^3)}=3^{27}\)

Next, the units digit of 3 in positive integer power repeats in pattern of 4: {3, 9, 7, 1}. So, the units digit of \(3^{27}\) (27=4*6+3) is the same as the units digit of \(3^3\), which is 7.


Answer: D
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Re: M09-32  [#permalink]

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New post 10 Apr 2016, 00:17
(27=4*6+3) so you add 4 + 3 = 7 (Please more details)
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Re: M09-32  [#permalink]

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New post 10 Apr 2016, 04:26
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Re M09-32  [#permalink]

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New post 06 Sep 2018, 01:16
I think this is a high-quality question and I agree with explanation. You have it as a Fractions/Ratios/Decimals question when it should be Exponents and Roots?
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Re M09-32  [#permalink]

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New post 17 Nov 2018, 08:03
I think this is a high-quality question and I agree with explanation.
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Re: M09-32  [#permalink]

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New post 13 Jan 2019, 01:40
I am not clear with the explanation as I know
3^3 * 3^3 * 3^3 = (3^3)^3 = 3^9

The question has (3^3)^3 what is equal to 3^9 and the unit digit of 3^9 is 3

Please give a details explanation with example. Thanks
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Re: M09-32  [#permalink]

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New post 13 Jan 2019, 03:17
smoni wrote:
I am not clear with the explanation as I know
3^3 * 3^3 * 3^3 = (3^3)^3 = 3^9

The question has (3^3)^3 what is equal to 3^9 and the unit digit of 3^9 is 3

Please give a details explanation with example. Thanks


I think you did not read the discussion above carefully enough.

The question does not ask about the units digit of \((3^3)^3\), it asks about the units digit of \(3^{3^3}\). The solution clearly explains the difference between these two expression. Please re-read.
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Re: M09-32   [#permalink] 13 Jan 2019, 03:17
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