Unit digit-how to find out?

[mystic87]

choices, choices, choices...
these are all great by the way. really makes you think about the properties of numbers.

[srm1234]

Hi friends, can anyone help me, to find the unit digit for 2^5^6^7?(2 power 5 power 6 power 6). Thanks

[ace_gre]

Hi,

This is how I would approach. Can anyone confirm the soundness of this?

First evaluate 2 ^5 = 32.
Take units digit of 32 = 2 ^6 = 64.
Take units digit again = 4^7 = 4.( 4 raised to even powers 2,4,6.. units digit is 6, 4 raised to odd powers is 4)

So unit's digit is 4. Is it the correct answer?

Thanks!