Remainder Problem -1

$$\eqalign{ & R\left( {\frac{{{{18}^{201}}}}{7}} \right) = ? \cr & = R\left( {\frac{{{6^{201}} \times {3^{201}}}}{7}} \right) \cr & = R\left( {\frac{{{{\left( { - 1} \right)}^{201}} \times {{\left( {{3^3}} \right)}^{67}}}}{7}} \right) \cr & = R\left( {\frac{{ - 1 \times {{\left( { - 1} \right)}^{67}}}}{7}} \right) \cr & = R\left( {\frac{{ - 1 \times - 1}}{7}} \right) \cr & = R\left( {\frac{1}{7}} \right) \cr & = 1 \cr} $$