Question

Find the last 2 digits of 9843^67483 ?
Also explain your method.....

Answer 1

67483 divide by four,find the remainder,the remainder is 3,then try 43 raise to 3,the last two digits will be 07 :)

Answer 2

Even I got the same explanation in Internet. Even your answer is correct.
Can you explain the logic behind this technique?

Answer 3

if you raise a number to nth term,there will be a pattern,and you should find that,you only need the last two digit,so only use 43,try raise 43 to 1,then raise 2, then raise 3, then raise 4,then when you raise it to 5,you will find out that the last two digits is like raise to 1,so therefore if it is raise to a large number,you just divide it by four and take the remainder :)

Answer 4

Hats off...
Again Maths showed its beauty
And thanks a lot @deac12 to help me see its admirable beauty...

Answer 5

you are welcome my friend :)