What is the ten’s digit of 7^195?
This question is based on the cyclicity concept in number theory.
Ten’s digit of powers of 7 follows a cyclic pattern as depicted:
7^1 = 07 7^5 = 16807
7^2 = 49 7^6 = 117649
7^3 = 343 7^7 = 823543
7^4 = 2401 7^8 = 5764801
Every fourth power of 7 has its ten’s place repeated.
Now, let’s break 195 (power of 7) into multiple of 4
195 = 48 * 4 + 3
The 7^195 will have its tens digit the same as 7^3 has, i.e. 4
Correct Answer: B
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