• # question_answer Find the numerical value of${{\left( 4096 \right)}^{\frac{-1}{4}}}.$ A)  16                              B)  8           C)  4                                D)  1

${{\left( 4096 \right)}^{\frac{-1}{4}}}={{\left( {{2}^{12}} \right)}^{-1/4}}={{2}^{\left( 12\times \frac{-1}{4} \right)}}={{2}^{-3}}=\frac{1}{8}$ Mathematical ingenuity: It is worthwhile to remember a few powers of 2 and $3:$ e.g., ${{2}^{2}}=4;{{.........2}^{6}}={{6}^{4}}......;{{....2}^{10}}=1024$ Similarly ${{3}^{2}}=9;\,{{3}^{3}}=27...;{{.....3}^{5}}=243,{{3}^{6}}=729$etc.