How to find last digits of any number of the firm a^b in a simple way?

Find the last digit of the number (13)^(12) .

Find the last two digits of the number 27^(27)dot

Write last two digits of the number 3^(400)dot

Write last two digits of the number 3^(400)dot

Find the last three digits of the number 27^(27)dot

Find the last two digits of the number (23)^(14)dot

How many 6-digit numbers are there?

How many 7-digit numbers are there?

How many 4-digit odd numbers can be formed using the digits 1,2,4 and 7 only once such that when the first and last digit are interchanged, the number is divisible by 4.

How many 7- digit numbers are there?