Exponents Help Pls

GRE Quant Problem Solving
1

The question is, “What is the tens digit of 7^241?”

Greg goes over this in one of his recorded lectures, but I’m still a little confused. I can see how there is a repeating pattern of 0,4,4,0,0,4,4… etc. However, I’m not sure how to identify the 241st placement in this pattern. Can someone please lend some assistance?

p.s. It’s my first time posting here, so if this is the wrong spot, I apologize.

2

7^1=07
7^2=49
7^3=343
7^4=2401
7^5=16807
So here you can see the pattern as 0,4,4,0 and then it repeats again 0,4,4,0. So this is a block of 4 digits that keeps repeating. So divide 241 by 4, remainder is 1. So look out for the tens digit of 7^1 which is 0. So the tens digit of 7^241 is 0.

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