Answer:
(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 \[\mathbf{1}{{\mathbf{0}}^{\mathbf{2}}}\] \[{{2}^{10}}=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=1024\] \[{{10}^{2}}=10\times 10=100\]. \[\because \] \[1024>100\] \[\therefore \] \[{{2}^{10}}>{{10}^{2}}.\]
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