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Q. Find the units digit of $(12)^{3^x}+(18)^{3 x}(x \in N)$.

Number System

Solution:

For all $x \in N$,
$(12)^{3^x}$ ends in either 8 or 2 and $(18)^{3^x}$ ends in either 2 or 8
If $(12)^{3^x}$ ends in 8 , then $(18)^{3^x}$ ends in 2 .
If $(12)^{3^*}$ ends in 2 , then $(18)^{3^*}$ ends in 8 .
$\therefore(12)^{3^x}+(18)^{3^x}$ ends in 0 only.