The units digit in the 7^126 is

Solution:

We know that if any number N can be expressed as

$\\ N\equiv x(mod10)$, where $\\ 0\leq x\leq 9$ , then the units digit in N is x

We have,

$\\ 7^2=49 \equiv 9(mod10) .......(1)\\ \\\Rightarrow 7^4=2401\equiv 1(mod10),\\ \\\Rightarrow (7^4)^31\equiv 1(mod10)\\ \\\Rightarrow 7^124\equiv 1(mod10).........(2)$

Multipying (1) and (2) , we get

$\\ 7^126\equiv 9(mod10)$

Unit's digit in $\\ 7^126$ is 9

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