What would be the digit at unit's place of $(13)^{547}$ ?

7

$(13)^{547}$

Note,

Every power repeats its unit digit after ever 4th power of itself.

So, we have to divide the power with 4 to get short form of power and the remainder we get will be considered as the original power of this number.

547/4 = 3 is the remainder.

$(13)^{3}$ = 7 will be the unit digit.