What is the last digit 3^3^3 ?
* 1
* 3
* 6
* 7
* 9
Guys, do you know any shortcut to do this kind of problem?
exponent???
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ok here is the shortcut..try a few examples using this and it wud be clear
lets say we need to find the unit digit of 3^256
consider this
3^1-unit digit 3
3^2-unit digit 9
3^3-unit digit 7
3^4-unit digit 1
now trick is 1^(whatever number)..the unit digit will always be 1
so express the given number in terms of 3^4
3^256=(3^4)^64--unit digit will be 1
In the given problem
3^3^3=3^9=3^8*3=(3^4)^2*3--unit digit will be 1*3=3
Hope I helped
lets say we need to find the unit digit of 3^256
consider this
3^1-unit digit 3
3^2-unit digit 9
3^3-unit digit 7
3^4-unit digit 1
now trick is 1^(whatever number)..the unit digit will always be 1
so express the given number in terms of 3^4
3^256=(3^4)^64--unit digit will be 1
In the given problem
3^3^3=3^9=3^8*3=(3^4)^2*3--unit digit will be 1*3=3
Hope I helped
The powers of two are bloody impolite!!
- ssmiles08
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IMO I got (D)
3^3^3 = 3^27
I believe if its (3^3)^3...only then it would be 3^9
you know the following order the exponents of 3 spits out as:
3 9 27 81
so the units digits are as following: 3 9 7 1
27 = 24 + 3
since 3^24 will have a units digit of 1 (since 24 is a multiple of 4); + 3 will have an units digit of 7.
3^3^3 = 3^27
I believe if its (3^3)^3...only then it would be 3^9
you know the following order the exponents of 3 spits out as:
3 9 27 81
so the units digits are as following: 3 9 7 1
27 = 24 + 3
since 3^24 will have a units digit of 1 (since 24 is a multiple of 4); + 3 will have an units digit of 7.
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I really really need to clarify this. i am always confusedssmiles08 wrote:IMO I got (D)
3^3^3 = 3^27
I believe if its (3^3)^3...only then it would be 3^9
you know the following order the exponents of 3 spits out as:
3 9 27 81
so the units digits are as following: 3 9 7 1
27 = 24 + 3
since 3^24 will have a units digit of 1 (since 24 is a multiple of 4); + 3 will have an units digit of 7.
so guys 3^3^3 ..what is it 3^9 or 3^27
oh by the way if it is 3^27
3^24*3^3..unit digit will be 7
The powers of two are bloody impolite!!
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Think about 3^3^3 like this:I really really need to clarify this. i am always confused
so guys 3^3^3 ..what is it 3^9 or 3^27
oh by the way if it is 3^27
3^24*3^3..unit digit will be 7
It's 3 raised to the 3^3 power, so it'll be 3^27.