Ответ:

[tex]1) {100}^{5} \div {1000}^{2} = {( {10}^{2} )}^{5} \div {( {10}^{3} )}^{2} = {10}^{10} \div {10}^{6} = {10}^{10 - 6} = {10}^{4} = 10000[/tex]

[tex]2) {8}^{3} \div {4}^{4} = {( {2}^{3}) }^{3} \div {( {2}^{2} )}^{4} = {2}^{9} \div {2}^{8} = 2[/tex]

[tex]3) \frac{ {4}^{3} \times {16}^{2} }{ {2}^{12} } = \frac{ {( {2}^{2}) }^{3} \times {( {2}^{4}) }^{2} }{ {2}^{12} } = \frac{ {2}^{6} \times {2}^{8} }{ {2}^{12} } = \frac{ {2}^{14} }{ {2}^{12} } = {2}^{2} = 4[/tex]

[tex]4) \frac{ {45}^{10} }{ {5}^{8} \times {3}^{19} } = \frac{ {5}^{10} \times {9}^{10} }{ {5}^{8} \times {3}^{19} } = \frac{ {5}^{10} \times {( {3}^{2}) }^{10} }{ {5}^{8} \times {3}^{19} } = \frac{ {5}^{10} \times {3}^{20} }{ {5}^{8} \times {3}^{19} } = {5}^{2} \times 3 = 25 \times 3 = 75[/tex]