[tex]b) {100}^{10} = {( {10}^{2} )}^{10} = {10}^{2 \times 10} = {10}^{20} [/tex]
[tex] {10}^{100} > {10}^{20} = > {10}^{100} > {100}^{10} [/tex]
[tex]c) {81}^{20} = {( {9}^{2}) }^{20} = {9}^{2 \times 20} = {9}^{40} [/tex]
[tex] {9}^{40} = {9}^{40} = > {9}^{40} = {81}^{20} [/tex]
[tex]d) {200}^{30} = {(100 \times 2)}^{30} = {100}^{30} \times {2}^{30} [/tex]
[tex] {8}^{10} \times {10}^{60} = {8}^{2 \times 5} \times {10}^{2 \times 6 \times 5} [/tex]
[tex] = {( {8}^{2} )}^{5} \times { ({10}^{12}) }^{5} = {( {8}^{2} )}^{5} \times {( {10}^{2} )}^{6 \times 5} [/tex]
[tex] = {8}^{2 \times 5} \times {10}^{2 \times 30} = {8}^{10} \times {100}^{30} = {( {2}^{3}) }^{10} \times {100}^{30} [/tex]
[tex] = {2}^{3 \times 10} \times {100}^{30} = {2}^{30} \times {100}^{30} [/tex]
[tex] {2}^{30} \times 100 = {2}^{30} \times 100 = > {200}^{30} = {8}^{10} \times {10}^{60} [/tex]
