• # question_answer 1) Identify the greater number, wherever possible, in each of the following? (i) ${{4}^{3}}$or ${{3}^{4}}$                    (ii) ${{5}^{3}}$or ${{3}^{5}}$                   (iii) ${{2}^{8}}$or ${{8}^{2}}$                       (iv) ${{100}^{2}}$or ${{2}^{100}}$

(i) ${{\mathbf{4}}^{\mathbf{3}}}$or ${{\mathbf{3}}^{\mathbf{4}}}$                 ${{4}^{3}}=4\times 4\times 4=64$                 ${{3}^{4}}=3\times 3\times 3\times 3=81$ $\because$     $81>64$ $\therefore$  ${{3}^{4}}>{{4}^{3}}$                 (ii) ${{\mathbf{5}}^{\mathbf{3}}}$or ${{\mathbf{3}}^{\mathbf{5}}}$                 ${{5}^{3}}=5\times 5\times 5=125$                 ${{3}^{5}}=3\times 3\times 3\times 3\times 3=81$ $\because$     $125>81$ $\therefore$  ${{5}^{3}}>{{3}^{5}}$                 (iii) ${{\mathbf{2}}^{\mathbf{8}}}$or ${{\mathbf{8}}^{\mathbf{2}}}$                 ${{2}^{8}}=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=256$    ${{8}^{2}}=8\times 8=64$ $\because$     $256>64$ $\therefore$  ${{2}^{8}}>{{8}^{2}}$.                 (iv) $\mathbf{10}{{\mathbf{0}}^{\mathbf{2}}}$or ${{\mathbf{2}}^{\mathbf{100}}}$                 ${{100}^{2}}=100\times 100=10000$                 ${{2}^{100}}={{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}\times {{2}^{10}}$$\times {{2}^{10}}\times {{2}^{10}}$                 $=1024\times 1024\times 1024\times 1024\times 1024\times 1024\times 1024$$\times 1024\times 1024\times 1024$ $\therefore$  ${{2}^{100}}>{{100}^{2}}$                 (v) ${{\mathbf{2}}^{\mathbf{10}}}$or $\mathbf{1}{{\mathbf{0}}^{\mathbf{2}}}$                 ${{2}^{10}}=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=1024$                 ${{10}^{2}}=10\times 10=100$. $\because$     $1024>100$ $\therefore$  ${{2}^{10}}>{{10}^{2}}.$