Question

Find the unit's place in the expansion $7^{131}$

Answer 1

The unit's place digit of $7^{131}$

$\Rightarrow 7^1=7$; $7^2=49$ ; $7^3=343$ ; $7^4=2401$

And thus the cycle of the unit's place is repeated after every $4^{th}$ power of $7$

$\therefore$ The unit's place digit of $7^{4\left(32\right)+3}$

$=$The unit's place digit of $7^3$

$=3$