Hello.
My name is sam. I am a student. The question is of a middle difficulty. You have answered this question already but you only answered to one digit.

What are the last TWO digits of:
3 to the power of 1994
7 to the power of 1994
3 to the power of 1994 + 7 to the power of 1994
7 to the power of 1994 - 3 to the power of 1994

 

Hi Sam,

You have probably seen our response to Landon's question which concerns the last digit of a large power of 7. The technique is very much the same for determining the last two digits of a large power and we will illustrate with 71994.

The list below contains the last TWO digits for the first 4 powers of 7. This
list repeats as the last two digits through all powers of 7.

07
49
43
01

This repeating list has a period of 4.
1994 = 498 4 + 2
The 2nd term in the list above is 49.
Therefore, the last two digits of 71994 is 49

Now try this technique for 31994. In this case you will have a much longer list before you find a repeat.

Paul and Penny