exponent???

[nhai2003]

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?

[tohellandback]

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

[ssmiles08]

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.

[tohellandback]

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.

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

[truplayer256]

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

Think about 3^3^3 like this:

It's 3 raised to the 3^3 power, so it'll be 3^27.

[nhai2003]

[spoiler] OA: D